Stats Exam 2 101 Questions

For a sample size of n=20, with s=5, we have constructed the following confidence interval for our estimate of the mean of normal distribution: 7.161 to 12.839. What confidence level did we use?

98% (101:9.8)

Nicole has determined that the average monthly sales at her rabbit store are normally distributed with a mean of 100 and a standard deviation of 20. Nicole wants to set an inventory level such that there is only a 5% chance of running out of stock. Where should nicole set the inventory level?

norminv(.95,100,20) or 132.9 (Berger 33)

Annalise Realty would like to develop a 99% confidence interval for the true average price of homes in Wrentham. She randomly selected 6 homes in Wrentham and found the following values: 237,000; 436,000; 550,000; 640,000; 660,000; 710,000 Use excel the find 99% confidence interval for the true average price of homes in Wrentham

$538,833 ± $290,778 (Berger 43)

Suppose that Abigail Faith buys one ticket to a lottery, the first ticket sold, which is labeled "#1". However, she doesnt know n, the total number of tickets sold. Reguardless of the value of n, one ticket will be randomly selected from the n tickets as the winning ticket. The prize is $1,000. Abagail does know that n, the number of tickets sold, is either 10 or 25 or 40, each with a ⅓ probability. What is the expected value of her winnings? (ignore what she pays for the ticket)

$55 (101:4.1)

Assume calls arrive at the switchboard following a Poisson distribution with mean u=3 calls per minute. What is the probability that during a 2 minute period we get more than three calls in one of the minutes and fewer than 2 calls in the other?

(1-Poisson(3,3,1)) * (Poisson (1,3,1) *2 (101:6.8)

Suppose that GMAT scores of applicants to a certain business school, ABC, are normally distributed with mean u=500 and standard deviation o=80. Suppose further that ABC automatically accepts any student whose GMAT score exceeds 700. The executive committee of the graduate admissions department is given only those applications with GMAT score over 540. What proportion of the applications received by the executive committee gets automatic acceptance?

(1Normdist(700,500,80,1)) / (1Normdist(540,500,80,1)) (101:7.5)

Suppose that 100 children came to your house to trick or trick this past Halloween. Half of them were boys. 20 of the girls that came to your house were dressed as a ballerina. Find a 95% confidence interval for the true proportion of girls that went out dressed as a ballerina. b) suppose that we want to estimate the true proportion of boys who dressed as vampires. We want to be 90% confident of being within .05 of the true p. What sample size is required?

.4 +/- .1358 b) 271 Berger p 215

A random sample of women business executives were asked whether they prefer Ms. as a title compared to Miss and Mrs. Out of 300 women polled, 261 said they preferred Ms. Find a 95% confidence interval for the true proportion of women business executives that prefer Ms. If we wanted to estimate the true proportion of women business executives who preferred the Ms. title within .02 with 95% confidence interval, what sample size of women business executives is needed? How would the answer change if we were certain the true proportion who prefer the Ms. title is no lower than .7?

.832 ---- .908 n = 2401; n = 2017 (Berger 45 and 46)

Bill, the manager of a paint supply store, wants to determine if the amount of paint contained in one-gallon cans purchased from a nationally known manufacturer actually averages 1 gallon. It is known that the standard deviation of the amount of paint in a can equals .02 gallons. A random sample of 50 cans is selected, and the mean was found to be .995 gallons. Find a 99% confidence interval for the true average amount of paint contained in 1-gallon cans from this nationally known manufacturer.

.995 +/- .0073 (the manufacturer is okay because 1 gallon is within this range. Berger self check p192

Suppose that the random varaible ,X, represents the number of marbles in a jar. If P(X=4)=.4 and P(X=6)=.6, what is the probability P(X=24)?

0 -already mutually exclusive and collectively exhaustive (Berger 22)

Blake Adams runs a sawmill where he turns local pine, spruce, and fir logs into boards and dimensional lumber. He has a large order for 14foot 2x8s for a skatingrink project. The logs are of random length. Blake knows that the length of these logs is normally distributed with a mean of 15 feet and a standard deviation of 2 feet. If there are 100 logs in the lot, what is the probability that more than 20 will be too short for this order?

1- Binomdist(20,100, normdist(14,15,2,1), 1) (101:7.1)

Suppose that at American Razor Corporation random sets of 100 razor blades are tested. A set is deemed acceptable if at least 98 of the 100 pass a sharpness test. The probability of any one blade passing the test is .99, and each blade is considered independent of each other blade. If ARC tests 50 sets of blades, what is the probability that at least 49 of the 50 sets are acceptable?

1- Binomdist(48,50,1-Binomdist (97,100,.99,1),1) (101:5.9)

Samuel Gilbert tests and inspects several batches of product per month. Each batch has 1,000 items in it, and each item is classified as either defective or good. The inspection of a batch consists of taking 20 randomly-selected products, with replacement, and determining how many of the 20 products are defective. A batch passes inspection if at most one of the 20 products are defective. If Sam inspects 15 batches in a given month, what is the probability that at least 14 of the 15 batches pass inspection?

1- binomdist(13,15,.9401,1)=.7743 (101:5.1)

Suppose that X, the length of a roll of yarn, is normally distributed with mean u=100 feet and standard deviation o=10 feet. If we take a random sample of four rolls of yarn, what is the probability that the longest of the four rolls has a length over 120 feet?

1-Binomdist(0,4,1-normdist(120,100,10,1),0/1) "how likely is it that at least one is over 120" so its 1-none (101:7.8)

Apples are very popular at Farmer's Markets in the fall. The Annibel Farmer's Market is an annual event that runs for four consecutive Saturdays in October. The weight of a crate of apples follows a normal distribution with a mean of 36 pounds and a standard deviation of 2.5 pounds. A fruit truck can hold 40 crates of fruit. If five trucks carrying crates of apples show up each Saturday for the Farmer's Market, what is the probability that each week over the course of the Annibel Farmer's Market that at least three of the five trucks have at most 10 crates that weigh under 30 pounds?

1-Binomdist(2, 5, Binomdist (10, 40, Normdist (30, 36, 2.5, 1), 1), 1)4 Parker Problem of the Day #1

thirty percent of beach goers in Lafayette bring a blanket to the beach. Forty percent bring a beach umbrella. On a random wednesday, 19 people come to the beach. What is the probability that more than 6 people brought a beach blanket? (answer with 2 separate excel equations)

1-binomdist(6,19,.3,1) binomdist(12,19,.7,1) (Quiz 4)

the time is takes to get a dozen toasted bagels with cream cheese at your local bakery is normally distributed with a mean of 6.5 minutes with a standard deviation of 1.5 minutes. On your way to work you want to bring in a dozen bagels to the office. You have taken a taxi and have asked the driver to wait while you get the order. The taxi driver says that he will have to charge you an extra $3 if he has to wait more than 5 minutes. What is the probability that you have the pay the taxi driver the $3? b) if they bakery wants to give a free cup of coffee to the customers who wait the longest 10%, what is the cutoff time to receive a complementary cup of coffee?

1-normdist(5,6.5,1.5,1)= .8413 b) normiv(.9,6.5,1.5)= 8.42 Quiz 5

Suppose we want to estimate the average weight of men in the US within 10 lbs. sigma is known to be 20 pounds. If we want to be 90% confident in our estimate, how large a sample size is required? b) in a production process, the average daily output per worker is needed in order to establish pay scales. It is assumed that output is normally distributed. A random sample of 20 workers was taken and x-bar=200 and s=30. Find a 90% confidence interval for the true mean output for the entire population of workers.

11 200 ± 11.598 (berger 40)

We sample n=120 people, and measure how long each person takes to fill out a certain form. We find that X-bar=13.85 minutes. Assume that we know from past data that o=1.56 minutes. Find a 99% confidence interval for the true average time (u) it takes a person to fill out the form

13.85 +/- .368 (I am 99% confident the true mean is between 13.482 and 14.218) Berger p190

The owner of Aleena's Poultry farm wants to estimate the number of eggs laid per chicken. A sample of 20 chickens shows they laid an average of 18 eggs per month with a standard deviation of 3 eggs per month. Find a 95% confidence interval for the population mean. Would it be reasonable to conclude that the population mean is 23 eggs?

18 ± 1.4 (Berger 42)

A randomly selected 25 SUV owners in the US were asked to report the miles per gallon of their SUV. the results revealed a mean of 18.2, with a sample standard deviation of 6.3. Find a 95% confidence interval for the true miles per gallon for SUVs.

18.2 ± 2.60 (berger 41)

A recent study by the New England Auto Dealers Association revealed that the mean profit per car sold for a random sample of 20 cars was $180 with a standard deviation of $30. Find a 95% confidence interval for the true average profit per car sold.

180 ± 14.04 (Berger 44)

You desire to estimate p for a binomial process. You know that p is less than .65 and greater than .45. Find n, the sample size required to yield 95% confidence of estimating the true proportion,p, within .02 .

2401 (101:9.9)

Jake Isaacson wishes to estimate p, the true proportion of college students who use a computer at least an hour per week. She wants to be 95% confident that the estimate she obtains is within .05 of the true value. What minimum sample size does Jane require? She knows from past studies that p is between .70 and .95.

323 (101:9.4)

the length of long distance telephone calls have a mean, u=12 minutes, and a standard deviation, o=4 minutes. If a random sample of 100 calls is selected, i) What is the probability that the sample mean, x-bar, is between 11 and 13 minutes? ii) What is the probability that the sample mean, x-bar, exceeds 12 minutes? iii) What is the probability that the sample mean, x-bar, exceeds 12.5 minutes? iv) What is the probability that the sample mean, x-bar, is under 11.2 minutes? v) There is a 90% chance that the sample mean, x-bar, will be above how many minutes? vi) the lowest 20% of the sample means will be below what number of minutes? vii) to answer the above questions, do you need to assume that the probability distribution of individual long distance phone call lengths is normally distributed? b) repeat the odd numbered sub-parts if the sample size is n=4, instead of n=100

35a) i) .9876 ii) .5 iii) .1056 iv) .0228 v) 11.484 vi) 11.664 vii) no, since n=100, CLT is invoked 35b) i) .3830 iii) .4013 v) 9.43 vii) yes, n<30, CLT is not invoked (Beger 35)

b) bank manager wants to estimate the average balance of a certain class of savings accounts. He samples a random selection of 30 accounts, and finds that x-bar= $6,780, and s=$1,100. Find a 95% confidence interval for the (true) average balance of all of the thousands of savings accounts at the bank of that certain class. c) find a confidence interval for the true mean of the normally distributed population from which a random sample of 6 is: 111999 d) repeat part c for data: 345567 e) in parts c and d the confidence levels have the same center. Why, then, are the confidence intervals so different? f) was the fact that the population probability distribution was stated to be normal necessary for you to solve parts C and D?

36b) $6,780 +/- 410.70 36c) 5 ± 4.598 36d) 5 ± 1.48 36e) standard deviations are different 36f) yes, n<30 (Berger 36)

Suppose we sample n=9 people and ask whether they agree or disagree with how the owner of the local baseball team is running the team. There is a 7-point scale and we find a mean of 4.41 and compute s to be .6. Find a 90% confidence interval for u.

4.41 +/- .372 Beger p200

The owner of the Regional Service Center wishes to estimate the true proportion of their customers who pay with a credit/debit card. He surveyed 100 customers and found that 75 paid with a debit/credit card. Estimate the value of the true population proportion. Find a 99% confidence interval for the true population proportion. b) Suppose you wish to estimate the proportion of men in the US who weigh over 200 pounds. You randomly sample 200 US men and find that 48 weigh over 200 pounds. Find a 95% confidence interval for the proportion of US men who weigh over 200 pounds.

47a) .75, .75 ± .11 47b) .24 ± .059 (berger 47)

Suppose that we want to estimate the average number of pitches thrown in an MLB game. We wish to be 95% confident that we get an estimate within 10 pitches of the true average, u. Suppose that we know from past data that o=40. What sample size do i require?

62 Beger p191

a consulting company has been called into evaluate the Boating Safety exam given by the state of New Hampshire. Demand to take the exam is very high with only 60% of the applicants admitted to take the exam per year. Data from the past three years and over 2,000 test takers, shows that scores on the exams are normally distributed with a mean of 140 and a standard deviation of 16. In addition they determined that it takes 30 minutes to take this 150 question exam on average with a standard deviation of 4 minutes. To further their understanding, the group did some analysis on some samples of 64 exams. A) Bill has decided to take the boating safety exam next month. If a passing score is getting at least "80" on the test. What score does he need to get to at least pass? B) How likely did the consulting company find a sample mean for exam scores of their samples to be greater than 144? C) The test taking facility in Concord is able to accommodate 50 people at a time to take the exam. They want to be as efficient as possible and want to get the room to turnover as quickly so to be able to offer more exam sessions. They decide that they want to have a time limit for the exam. The cutoff is set for 38 minutes. How many people will not finish the exam within the allotted time on average?

A) norminv(.8,140,16)=153.44 B) 1-normdist(144,140,2,1)=.0228 C) 1-normdist(38,30,4,1)=1.114

Blindfolded, Victor Schena reaches into a fishbowl and grabs a fish. Vic can grab a goldfish with probability of .4, and Angelfish with probability of .2, a Tetra fish with a probability of .1, and a Black Molly with a probability of .3. Each time, he returns the fish undamaged to the bowl. What is the probability that, in 150 grabs, the number of times Vic catches a Goldfish will be atleast 50 and at most 70?

Binomdist(70,150,.4,1) - Binomdist(49,150,.4,1)= .920272 (101:5.4)

The Chuck River Regatta is a sailboat race between three countries and held every Spring. The winner is determined by the team that wins the majority of 15 races held over a twenty day period. America's team was the favorite but not doing well. The America team knew that their average time per race was normally distributed with a mean of 70 minutes with a standard deviation of 3 minutes. It was the day of the 8th race and the America team had not won any of the daily races to this point. They would need to win all the remaining races to win the Regatta. They also calculated that that they would need to have their race time in the lowest 20% of their race time distribution to ensure they win the race. What is the probability the America team wins given we know that they were faster than their average race time? (Use Excel for the whole answer)

Binomdist(8,8,(Normdist(Norminv(.2,70,3),70,3,1)|.5),0) Parker Problem of the Day #2

Suppose that the number of cars entering a car wash on Thursday mornings in the summertime is Poisson distributed with a mean of u=6/hour. If the car wash opens at 9am, what is the probability that the 9th car to arrive at the car wash on a random Thursday morning in the summer arrives after 10am?

Poisson (8,6,1)= .8472 (101:6.2)

Suppose the number of phone calls that a business receives is Poisson distributed with mean u=6/hr. What is the probability that the business has 5 straight halfhour periods in which each halfhour has no more than 2 calls?

Poisson(2,3,1)^5 OR binomdist(5,5, (poisson2,3,1),0) (101:6.6)

Suppose that the weight of men in the US is normally distributed with u=175 pounds and o=25 pounds. What is the probability of a randomlyselected man weighing more than 200 pounds given that we know his weight is above average?

[1-Normdist(200,175,25,1)]/.5=.3174 (101:7.11) ** Parker says this is an important question

A teacher gave her students a multiple choice exam consisting of 10 questions. Fiona, a student, has determined that she needs 8 or more out of 10 questions to recieve at least a B for the course. Fiona has also determined that she has an 80% chance of getting any one question correct, and each question is independent of each other question. WHen Fiona saw her teacher later that day in the hallway she asked her teacher what she scored on the exam. The teacher replied that she does not remember the exact score, but she does remember that she definitely passed the exam. If a passing grade is at least 6 correct, what is the probability that Fiona will get at least a B for the course?

[1-binomdist(7,10,.8,1)] / [1-binomdist(5,10,.8,1)]=.701 (101:5.8)

The number of students that come to Professor Smith's office hours is at a rate of 10 per hour. What is the probability that on a random Tuesday Professor Smith gets more than 5 students arriving in the first half hour and less than 5 in the second half hour?

[1-poisson(5,5,1)] * poisson(4,5,1)

a) a machine produces rolls of tape of any desired width and length. It is known that the machines capability is such that the standard deviation of the width of an individual roll is .05 inches. If a random sample of 100 rolls of tape indicates a sample mean of .5 inches, find a 95% confidence interval for the true mean of the order of (over 1 million) rolls. Do we need to assume that the distribution of widths is normally distributed? Discuss. b) if we wanted to estimate the mean of the process within .005 inches, with a 95% confidence, what sample size of rolls would we need? How can you most easily determine whether it is more than the n=100 of part a

a) .5 ± .0098 b) n = 385 (berger 37 and 38)

Suppose that the number of lighting strikes per year at the AFB Golf course in Boca Raton, FL is Poisson distributed with a mean of 7. a) Whats the probability that a given year at AFB has more than 10 lighting strikes? b) Whats the probability that a given year at AFB has fewer than 10 lighting strikes? c) Do the answers to A and B add to 1? Why? d) Starting with next year, what is the probability that AFB encounters a year of above average number of lightning strikes before it encounters a year of below average number of lightning strikes?

a) 1 - Poisson(10, 7, 1) b) Poisson(9, 7, 1) c) no. it omits X = 10 d) {1 - Poisson(7, 7, 1)}/{1 - Poisson(7, 7, 0)} ** D will not be on the test, dont worry about it- Parker (berger 29)

The number of arrivals at a walk-in clinic in the 9am- noon time period on a weekday follows a Poisson distribution with mean, 8/hour. a) whats the probability that there are more than 20 arrivals during a randomly selected 9am- noon weekday time period? b) what is the probability that during a particular 9am-noon weekday time period,each of the three individual hours has at least 7 arrivals? c) what is the probability that during a particular 9am-noon weekday time period, exactly one of the three individual hours has more than 12 arrivals?

a) 1 - Poisson(20, 24, 1) b) {1 - Poisson(6, 8, 1)}3 = binomdist(3, 3, 1-Poisson(6, 8, 1), 0) c) binomdist(1, 3, 1-Poisson(12, 8, 1), 0) (Berger 28)

Assume that the length of time needed to renew your license at the Mass. RMV is normally distributed with a mean u=50 minutes, and a standard deviation o=10 minutes. a) what the probability that a randomly selected person will require more than 65 minutes to renew their license? b) what the probability that a randomly selected person will require less than 40 minutes to renew their license? c) what the probability that a randomly selected person will require between 45 and 55 minutes to renew their license? d) assume that the length of time needed to renew their license at the Mass RMV is normally distributed with mean u=50, and a standard deviation o=10 minutes. If the RMV wishes to give a discount to those 10% of customers who wait the longest, what is the cutoff to get the discount? e) the RMV wishes to launch a new PR campaign. Their slogan is "95% of all customers will have their license renewed in under ___ minutes. Fill in the blank

a) 1 - normdist(65,50,10,1) or .0668 b) normdist(40,50,10,1) or .1587 c) normdist(55,50,10,1) - normdist(45,50,10,1) or .3830 d) norminv(.90,50,10) or 62.82 e) norminv(.95,50,10) or 66.45 (Berger 32)

Assume that the amount spent by fans at Patriot's games for food and drinks is normally distributed with a mean u=$32 and o=$8. If 60,000 people attend a given game, how many would be expected to spend more than $44? b) if we randomly select 10 fans leaving a patriots game, what is the probability that exactly 3 spent above $44?

a) 1-normdist(44,32,8,1) b) binomdist(3,10,.0668,0) Berger Self Check pg 165

A research firm conducted a survey to determine the mean amount of time teenagers spend each day texting. The standard deviation is known to be 12 minutes. A sample of 36 teenagers revealed a sample mean of 42 minutes. a) what is the point estimate of the population mean? b) find a 95% confidence interval estimate for u? c) repeat the exercise above, this time with a sample of 64 teenagers. What now is the 95% confidence interval estimate for u? Compare your answer with the previous problem. Which interval has more confidence? Which interval has more precision?

a) 42 b) 42 ± 3.92 c) 42, 42 ± 2.94, same confidence, increased precision (Berger 39)

Liam's Shaving Cream ads claim that 25% of all men aged 30-54 favor its brand. You select a random sample of 20 men in that age bracket. Assuming the claim is true: a) what is the expected number of men who favor Liam's brand? b) what is the probability of finding exactly 8 men who favor Liam's brand? c) what is the probability of finding at least 2 men who favor Liam's brand? d) if you sample 10 men today and 10 men tomorrow, what is the probability that each day more than 4 men favor the brand?

a) 5 men b) binomdist(8,20,.25,0) c) 1-binomdist(1,20,.25,1) d) [1-binomdist(4,10,.25,1)]^2 (Berger self check pg 134)

Professor Taylor is a statistics professor, holds office hours every Thursday. Students arrive at her office at the rate of 10 per hour. The number of arrivals follows a Poisson distribution. a) What is the probability that no students will arrive in a particular hour? b) Whats the probability that at least 3 arrive in a particular hour? c) whats the probability that at most 5 will arrive in a particular hour?

a) Poisson(0,10,0) b) 1-Poisson(2,10,1) c) Poisson(5,10,1) (Berger 30)

Scoring for the King Philip 6th grade basketball team follows a Poisson distribution with a rate of 1.5 points scored per minute and each quarter in the 6th grade league last 8 minutes. a) whats the probability of the team scoring exactly 10 points in a quarter? b) scoring 12 points in a given quarter? c) if you assume that each quarter in a game is independent of any other, what is the probability of the King Philip team scoring over 10 points for exactly 3 out of 4 quarters of a game?

a) Poisson(10,12,0) b) Poisson(12,12,0) c) binomdist(3,4,1-poisson(10,12,1),0) (Berger 31)

Noel plays basketball for the King Phillip Metrowest Basketball Team. When a player in basketball gets fouled he is often awarded free throws to attempt. Assume that Noel makes 75% of his free throws and that each free throw attempt is independent of any prior free throw attempt Noel has taken. If Noel takes 10 free throw attempts in a game, what is the probability that he makes: a) all 10? b) exactly 6? c) less than 5? d) more than 7? e) at least 8? f) at most 4?

a) binomdist(10,10,.75,0) b) binomdist(6,10,.75,0) c) binomdist(4,10,.75,1) d) 1-binomdist(7,10,.75,1) e) 1-binomdist(7,10,.75,1) f) binomdist(4,10,.75,1) (berger 24)

Suppose that a certain target market has 10% response rate to a catalog sent out by a well known clothing store. Suppose a special audit is done on 100 randomly selected recipients of the catalog. a) what is the probability that among the 100 there are exactly 11 responses? b) What is the probability that among the 100 there are at least 11 responses? c) What is the probability that among the 100 there are at least 11 responses, given we know we got at least the expected number of responses? d) If we know that the company received only one response from the first 90 recipients audited, what is the expected number of responses from the last 10 receipts to be audited?

a) binomdist(11, 100, .1, 0) b) 1 - binomdist(10, 100, .1, 1) c) {1 - binomdist(10, 100, .1, 1)}/ {1 - binomdist(9, 100, .1, 1)} d) 1 (Berger 27)

In a recent study, 70% of homes in the US were found to have a laptop computer. In a random sample of 12 homes, what is the probability that: a) all 12 have a laptop? b) only 9 have a laptop? c) at least 6 have a laptop? d) more than 8 have a laptop? e) if you randomly sample 12 homes today and 12 homes tomorrow, what is the probability that you will find at least 6 have laptops each day?

a) binomdist(12,12,.7,0) b) binomdist(9,12,.7,0) c) 1-binomdist(5,12,.7,1) d) 1-binomdist(8,12,.7,1) e) (1-binomdist(5,12,.7,1))^2 (Berger 25)

a) the computer help desk knows that 30% of employees need help logging onto the Internet. What is the probability that out of 14 employees that less than 3 people will need help logging in? b) If every Wednesday there are exactly 18 employees who come into the help desk, what is the probability that exactly 6 people will need help over 4 Wednesdays?

a) binomdist(2,14,.3,1) b) binomdist(6,18,.3,0)^4 Quiz 4

Consider the following distribution: x f(x) 1 .3 3 .4 4 .3 a) if we changed exactly one of the values of X, leaving everything else the same, is u (mu) guaranteed to change? b) if we changed exactly one of the values of X, leaving everything else the same, is o (sigma) guaranteed to change?

a) yes b) no (Berger 23)

a)Assume that arrivals at a local restaurant are Poisson distributed with a mean of 8 per hour. If the restaurant is open for 6 hours per day, what is the probability of at least 50 customers on a given day? b) what is the probability of getting exactly 3 days out of 5 (randomly selected) with at least 50 customers each day?

a)1- poisson(49,48,1) b) binomdist[3,5,1-poisson(49,48,1),0] (Berger Self-Check 143)

Suppose that 55% of all people prefer Coke to Pepsi. If we randomly sample 400 people, what is the probability that the majority of the respondents indicate a preference for Pepsi? Assume each persons opinion is independent

binomdist(199, 400, .55, 1) OR 1 - binomdist(200, 400, .45, 1) (Berger 26)

Abigail and Jared Direct Case

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Lin DVD Case

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Lotus Blossom Hotel Case

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The daily amount of time that teenagers spend playing XBOX follows a normal distribution. However, the mean and the standard deviation are unknown. 40% of the time, playing time exceeds 48 minutes, 10% of the time, playing time exceeds 60 minutes. What is the mean and standard deviation?

µ = 45.09, σ = 11.65 ** parker doesnt think this will be on the test (berger 34)