Quiz 4 lessons 15-20, Math 105

Find the probability of guessing the top five winners​ (in any​ order) from a group of 17 finalists in a spelling bee.

1/6188

Find the probability of being dealt 5 cards from a standard​ 52-card deck, and the cards are a 8​, 9​, 10​, jack​, and queen​, all of the same sui

1/649,740

Question content area top Part 1 Suppose that an urn contains 3 black ​marbles, 8 green ​marbles, and 9 white marbles. If one marble is​ selected, determine the probability that it is green.

2/5

How many anagrams​ (rearrangements) of the letters CAMPHONE can you​ make?

40,320

Pizza House offers 4 different​ salads, 4 different kinds of​ pizza, and 4 different desserts. How many different three course meals can be​ ordered?

64

A certain lottery has 28 numbers. In how many different ways can 5 of the numbers be​ selected? (Assume that order of selection is not​ important.)

92,280 differnet ways the numebers can be selected

A report claims that the returns for the investment portfolios with a single stock have a standard deviation of 0.52​, while the returns for portfolios with 35 stocks have a standard deviation of 0.331. Explain how the standard deviation measures the risk in these two types of portfolios.

A lower standard deviation means more certainty in the return and less risk.​ Hence, the returns for portfolios with 35 stocks have less risk than the ones with a single stock.

What do we mean when we say that a distribution is​ symmetric?

A​ single-peaked distribution is symmetric if its left half is a mirror image of its right half.

How many different telephone numbers of the form ​aaa-bbb-cccc can be formed if the area code aaa cannot contain 8 and the prefix bbb cannot contain 3​?

B. Arrangements with repetitions because there are r selections from a group of n choices and choices can be repeated. here are 5,314,410,000 different telephone numbers.

How many possible birth orders with respect to gender are possible in a family with four ​children? (For​ example, BBGG and GGBG are different​ orders.)

C. Arrangements with repetitions because there are r selections from a group of n choices and choices can be repeated. 16 possible birth orders for a family with four children

A dog shelter is giving away 9 different​ dogs, but you have room for only 5 of them. How many different dog families could you​ have?

Combinations should be used because no item may be selected more than once and the order does not matter.

Exam results for 100 students are given below. For the given exam​ grades, briefly describe the shape and variation of the distribution. median=74​, mean=80​, low score=62​, high score=90

The distribution is right skewed and has low variation.

State, with an​ explanation, whether you would expect the following data set to be normally distributed. The delay in departure of trains from a station​ (note that​ trains, buses, and airplanes cannot leave​ early)

This data set is not normally distributed. There is no reason to assume that the​ mean, median, and mode of this distribution are centered at a central peak in a​ symmetric, bell-shaped distribution. It is possible that trains never experience delay or frequently encounter very above average delays at this particular station.

In my data set of 10 exam​ scores, the median turned out to be the score of the person with the third highest grade. No two people got the same score.

This does not make sense because the median value should be between the fifth and sixth highest scores.

Decide whether the following statement makes sense​ (or is clearly​ true) or does not make sense​ (or is clearly​ false). Explain your reasoning. Both exams had the same​ range, so they must have had the same median.

This does not make sense because the range is the difference between the highest and lowest data values. It has nothing to do with the median.

Suppose you read that the average height of a class of 36 ​eighth-graders is 45 inches with a standard deviation of 42 inches. Is this​ likely? Explain.

This is not likely because a mean of 45 and a standard deviation of 42 would imply that about​ 5% of the heights differ from the mean by more than 84​, which is impossible

My professor graded the final score on a​ curve, and she gave a grade of A to anyone who had a standard score of 2 or more.

This makes sense because a standard score of 2 or more corresponds to roughly the 97th percentile. Though this curve is stingy on giving out​ A's to​ students, it is still giving the top students the highest grade.

The weights of babies born at Belmont Hospital are normally distributed with a mean of 6.8 pounds and a standard deviation of 7 pounds.

does not make sense

Define the​ five-number summary, and explain how to depict it visually with a boxplot. Which five numbers are included in the​ five-number summary for a data​ set? Explain how to depict the five numbers visually with a boxplot. Choose the correct answer below. Select all that apply.

low​ value, lower​ quartile, median, upper​ quartile, and high value Draw a number line that spans all the values in the data set. Enclose the values from the lower to upper quartile in a box. Draw a vertical line through the box at the median. Add​ "whiskers" extending to the low and high values.

Cans of soda vary slightly in weight. Given below are the measured weights of seven​ cans, in pounds. Find the mean and median of these weights.​ Which, if​ any, of these weights would be considered an​ outlier? What are the mean and median weights if the outlier is​ excluded? 0.8161 0.8192 0.8164 0.8177 0.7903 0.8142 0.8121

mean= 0.81229 median= 0.8161 outlier= 0.7903 mean without outlier= 0.81595 median without outlier= 0.81625

Find the mean and median for the waiting times at Big Bank given below. Show your work​ clearly, and verify that both are the same. The following values are measured in minutes. Big Bank​ (three lines): 4.1 5.2 5.6 6.2 6.7 7.2 7.7 7.7 8.5 9.3 11.0

mean= 7.2 median is the 6th value in the sorted data set median is 7.2

The trifecta at most racetracks consists of selecting the​ first-, second-, and​ third-place finishers in a particular race in their proper order. If there are ten entries in the trifecta​ race, how many tickets must you purchase to guarantee a​ win?

must purchase 720 tickets

An experiment consists of drawing 1 card from a standard​ 52-card deck. What is the probability of drawing a diamond​?

the probability of drawing a diamond is 1/4

What is a normal​ distribution? Briefly describe the conditions that make a normal distribution.

A normal distribution is a​ symmetric, bell-shaped distribution with a single peak. Its peak corresponds to the​ mean, median, and mode of the distribution. Its variation is characterized by the standard deviation of the distribution.

What is a standard​ score? How do you find the standard score for a particular data​ value? Choose the correct definition of a standard score below. Choose the correct formula for computing a standard score below

A standard score is the number of standard deviations a data value lies above or below the mean. D. The standard score for a particular data value is given by z= data value−mean/ standard deviation.

How many different eight​-digit passwords can be formed from the numbers zero to seven if repetition is not​ allowed?

A. Permutations should be used because no item may be selected more than once and the order matters.

What are​ outliers? Describe the effects of outliers on the​ mean, median, and mode.

An outlier in a data set is a value that is much higher or much lower than almost all other values. An outlier can change the mean of a data​ set, but does not affect the median or mode.

How many different four​-digit codes can be formed using digits 0 through​ 9?

Arrangements with repetitions because there are r selections from a group of n choices and choices can be repeated. There are 10,000 possible codes.

How many license plates can be made of the form XX​-YYY​, where X is a letter of the alphabet and Y is a numeral​ 0-9?

Arrangements with repetitions because there are r selections from a group of n choices and choices can be repeated. There are 676,000 possible license plates.

Choose the best answer to the following question. Explain your reasoning with one or more complete sentences. Suppose you toss one coin three times in a row and get​ heads, tails, heads​ (HTH). If you are interested in the number of heads that​ appear, which one of the following sets of three tosses has a different outcome but corresponds to the same event as the first set of​ tosses?

HHT, because it has the same number of heads and tails as HTH.

What does it mean when we write​ P(A)? What is the possible range of values for​ P(A), and​ why?

P(A) means the probability that event A will occur. The range of possible values for​ P(A) is from 0 to 1​ (inclusive), with 0 meaning there is no chance that event A will occur and 1 meaning it is certain that event A will occur

Suppose there is a bag containing 15 pink marbles ​(P​), 15 indigo marbles ​(I​), 15 black marbles ​(B​), and 15 yellow marbles ​(Y​). Someone mixes the marbles​ thoroughly, draws one marble at​ random, puts the marble back in the​ bag, mixes the bag​ thoroughly, and draws another marble at random. Complete parts​ (a) and​ (b) below.

P​,PI​,PB​,PY​,IP​,II​,IB​,IY​,BP​,BI​,BB​,BY​,YP​,YI​,YB​,YY

What is the probability a baseball player with a 0.306 on-base percentage ​(defined as times on base divided by plate appearances​) will get on base in his next plate appearance​?

Relative frequency method probability is 0.306

Give a simple example of a symmetric distribution. Choose the correct answer below.

The heights of a sample of 100 women is a symmetric distribution.

For the following​ distribution, decide whether you expect the​ mean, median, or mode to give the best representation of the center of the​ distribution, and explain why. The individual weights of oranges in a​ 5-pound bag.

The mean because there are likely to be few outliers.

The numbers of words defined on randomly selected pages from a dictionary are shown below. Find the​ mean, median, and mode of the listed numbers. 48, 37, 59, 50, 55, 68, 61, 57, 35, 74 What is the​ mean? Select the correct choice below​ and, if​ necessary, fill in the answer box within your choice.

The mean is 54.4

Actual times​ (in seconds) recorded when statistics students participated in an experiment to test their ability to determine when one minute​ (60 seconds) had passed are shown below. Find the​ mean, median, and mode of the listed numbers. 53 52 75 65 67 60 48 48

The mean is 58.5 The median is 56.5 The mode is 48 seconds

Choose the correct description of the mean below.

The mean is the sum of all the values divided by the number of values. It can be strongly affected by outliers

After recording the pizza delivery times for two different pizza​ shops, you conclude that one pizza shop has a mean delivery time of 46 minutes with a standard deviation of 3 minutes. The other shop has a mean delivery time of 43 minutes with a standard deviation of 18 minutes. Interpret these figures. If you liked the pizzas from both shops equally​ well, which one would you order​ from? Why? Interpret these figures. Choose the correct answer below. If you liked the pizzas from both shops equally​ well, which one would you order​ from? Why? Choose the correct answer below.

The means are nearly​ equal, but the variation is significantly greater for the second shop than for the first. hoose the first shop. The delivery time is more reliable because it has a lower standard deviation.

For the following​ distribution, decide whether you expect the​ mean, median, or mode to give the best representation of the center of the​ distribution, and explain why. Per capita earnings in New York City.

The median because it is unaffected by outliers.

The numbers of words defined on randomly selected pages from a dictionary are shown below. Find the​ mean, median, and mode of the listed numbers. 48, 37, 59, 50, 55, 68, 61, 57, 35, 74 What is the​ median? Select the correct choice below​ and, if​ necessary, fill in the answer box within your choice.

The median is 56

Choose the correct description of the median below.

The median is the middle value in a data set. It is not affected by outliers.

Choose the correct description of the mode below.

The mode is the most common value in a data set. It is not affected by outliers.

Give a simple example of a​ right-skewed distribution. Choose the correct answer below.

The number of books read during the school year by fifth graders is a​ right-skewed distribution.

What are the quartiles of a​ distribution? How do we find​ them? What are the quartiles of a​ distribution? How do we find​ them?

The quartiles are values that divide the data distribution into quarters. The lower quartile is the median of the data values in the lower half of a data set. The middle quartile is the overall median. The upper quartile is the median of the data values in the upper half of data set.

Give a simple example of a​ left-skewed distribution. Choose the correct answer below.

The speed of cars on a road where a visible patrol car is using radar to detect speeders is a​ left-skewed distribution.

The probability of drawing an ace or a spade from a deck of cards is the same as the probability of drawing the ace of spades.

The statement does not make sense because there is one card that is the ace of spades but more than one card that is either an ace or a spade.

Linda used the permutations formula to determine how many possible relay orders could be made with the 10 girls on her swim team.

The statement makes sense because all selections come from the same swim​ team, each girl can be selected only​ once, and the order matters.

I made a distribution of 15 apartment rents in my neighborhood. One apartment had a much higher rent than all of the​ others, and this outlier caused the mean rent to be higher than the median rent.

The statement makes sense because an outlier with a large value increases the​ mean, but does not affect the median.

Decide whether the following statement makes sense​ (or is clearly​ true) or does not make sense​ (or is clearly​ false). Explain your reasoning. For the 30 students who took the​ test, the high score was​ 80, the median was​ 75, and the low score was 40.

The statement makes sense because it is possible that when sorting the 30 scores from low to​ high, the first value was​ 40, the highest value was​ 80, and 75 was halfway between the 15th and the 16th score.

The number of different possible batting orders for 9 players on a​ 25-person baseball team is so large that​ there's no hope of trying them all out.

The statement makes sense because substituting n=25 and r=9 into the formula nPr=n!(n−r)! results in more than 700 billion batting orders.

In a data set of 10 exam​ scores, in which no two people got the same​ score, the mean was equal to the score of the person with the third highest grade.

The statement makes sense because the data could be skewed towards the higher​ scores, causing the mean to be equal to the third highest grade.

A DJ is preparing a playlist of 16 songs. How many different ways can the DJ arrange the first five songs on the​ playlist?

There are 524,160 different ways that the DJ can arrange the first five songs on the playlist.

The numbers of words defined on randomly selected pages from a dictionary are shown below. Find the​ mean, median, and mode of the listed numbers. 48, 37, 59, 50, 55, 68, 61, 57, 35, 74 What​ is(are) the​ mode(s)? Select the correct choice below​ and, if​ necessary, fill in the answer box within your choice.

There is no mode.

Consider the distribution of exam scores​ (graded from 0 to​ 100) for 79 students when 40 students got an​ A, 24 students got a​ B, and 15 students got a C. Complete parts​ (a) through​ (d) below. a. How many peaks would you expect for the​ distribution? b. Make a sketch of the distribution. Choose the correct answer below. c. What shape would you expect for the​ distribution? d. What variation would you expect in the​ distribution?

There would probably be one peak because there are no obvious reasons why the exam scores would form different groups. B. The distribution would probably be​ left-skewed because many of the students got an​ A, and very few got a C. d. answer: The variation would probably be large because many students got an​ A, some got a​ B, and a small number got a​ C, and so the data are not clustered.

Consider the distribution of the annual rainfall in 95 cities selected randomly throughout the United States. Complete parts​ (a) through​ (d) below. a. How many peaks would you expect for the​ distribution? c. What shape would you expect for the​ distribution? d. What variation would you expect in the​ distribution?

There would probably be one peak because there are no obvious reasons why the values of the annual rainfall would form different groups. The distribution would probably be​ right-skewed because there is a clear minimum amount of rainfall but no obvious maximum amount. The variation would probably be large because there would likely be several cities with very different amounts of rainfall.

Consider the distribution of the monthly sales of rain ponchos over a​ one-year period at a store in Niagara Falls ​(the distribution will look best if you start from January​). Complete parts​ (a) through​ (d) below. a. How many peaks would you expect for the​ distribution? c. What shape would you expect for the​ distribution? d. What variation would you expect in the​ distribution?

There would probably be one peak corresponding to the summer months. The distribution would probably be symmetric because the distribution of monthly sales of rain ponchos has its peak in the summer months when more people visit Niagara Falls. The variation would probably be large because there would likely be several months with very different numbers of rain ponchos sold.

The heights of male basketball players at a local college are normally distributed with a mean of 6 feet 3 inches and a standard deviation of 3 inches.

makes sense

Suppose you study family income in a random sample of 400 families. Your results can be summarized as the mean family income was ​$42,000​, the median family income was $32,000​, the highest and lowest incomes were $252,000 and $2,300​, respectively. Describe the distribution as​ symmetric, left-skewed, or​ right-skewed. Choose the correct answer below. How many families in the sample earned less than ​$32,000​? Explain how you know. Choose the correct answer below. Based on the given​ data, can you determine how many families earned more than $42,000​? Why or why​ not? Choose the correct answer below.

right-skewed ​200 families, because the median is the middle value in the sorted data set. ​No, because the number of families that earned more than $42,000 depends on the distribution.

Decide which method​ (theoretical, relative​ frequency, or​ subjective) is​ appropriate, and compute or estimate the following probability. An experiment consists of drawing 1 card from a standard​ 52-card deck. What is the probability of drawing a red 9​? Which method is​ appropriate? The probability of drawing a red 9 is

the theoretical method 1/26

decide which method​ (theoretical, relative​ frequency, or​ subjective) is​ appropriate, and compute or estimate the following probability. A card is drawn at random out of a​ well-shuffled deck of 52 cards. Find the probability of drawing an eight, nine, or ten.

the theoretical method 3/13

Rolling a sum of 4 when you roll two dice

the theoretical method should be used. the probability of rolling a sum of 4 is 1/12

You are required to take five​ courses, one each in​ humanities, sociology,​ science, math, and music. You have a choice of 3 humanities​ courses, 3 sociology​ courses, 5 science​ courses, 6 math​ courses, and 7 music courses. How many different sets of five courses are​ possible?

there are 1890 different sets of five courses possible.

Choose the best answer to the following question. Explain your reasoning with one or more complete sentences. Suppose that four​ 6-sided dice are tossed. How many outcomes are​ possible?

​6x6x6x6, because each of the four dice have six possible outcomes.