Finance 208 Homework 3

True or False: A normal probability plot may be used to assess the assumption of normality for a particular set of data.

True

True or False: Another name for the mean of a probability distribution is its expected value.

True

True or False: Any set of normally distributed data can be transformed to its standardized form.

True

True or False: If π remains constant in a binomial distribution, an increase in n will increase the variance.

True

True or False: Theoretically, the mean, median, and the mode are all equal for a normal distribution.

True

For sample sizes greater than 30, the sampling distribution of the mean will be approximately normally distributed

regardless of the shape of the population.

True or False: As the sample size increases, the standard error of the mean increases.

False

True or False: If a data set is approximately normally distributed, its normal probability plot would be S-shaped.

False

True or False: The Poisson distribution can be used to model a continuous random variable.

False

Which of the following about the binomial distribution is not a true statement?

The variable of interest is continuous.

A lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the lab conducts. Prices for 100 rats follow the following distribution: Price:$10.00$12.50$15.00 Probability:0.350.400.25 How much should the lab budget for next year's rat orders be, assuming this distribution does not change?

$637

For some value of Z, the value of the cumulative standardized normal distribution is 0.2090. The value of Z is

-0.81

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a certain year in the past. Suppose a sample of 100 major league players was taken. Find the approximate probability that the mean salary of the 100 players exceeded $3.5 million.

.0228

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a certain year in the past. Suppose a sample of 100 major league players was taken. What was the standard error for the sample mean salary?

.12 million

SCENARIO 5-6The quality control manager of Green Bulbs Inc. is inspecting a batch of energy saving compact fluorescent light bulbs. When the production process is in control, the mean number of bad bulbs per shift is 6.0.Referring to Scenario 5-6, what is the probability that any particular shift being inspected has produced 4.0 bad bulbs.

.1339

SCENARIO 7-5According to an article, 19% of the entire population in a developing country have high-speed access to the Internet. Random samples of size 200 are selected from the country's population.Referring to Scenario 7-5, the population mean of all the sample proportions is ________.

.19

If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, find the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 3 minutes.

.3085

SCENARIO 7-1The time spent studying by students in the week before final exams follows a normal distribution with a standard deviation of 8 hours. A random sample of 4 students was taken in order to estimate the mean study time for the population of all students.Referring to Scenario 7-1, what is the probability that the sample mean exceeds the population mean by more than 2 hours?

.3085

The amount of tea leaves in a can from a particular production line is normally distributed with μ = 110 grams and σ = 25 grams. What is the probability that a randomly selected can will contain less than 100 grams of tea leaves?

.3446

SCENARIO 5-6The quality control manager of Green Bulbs Inc. is inspecting a batch of energy saving compact fluorescent light bulbs. When the production process is in control, the mean number of bad bulbs per shift is 6.0.Referring to Scenario 5-6, what is the probability that any particular shift being inspected has produced at least 6.0 bad bulbs.

.5543

SCENARIO 7-3The lifetimes of a certain brand of light bulbs are known to be normally distributed with a mean of 1,600 hours and a standard deviation of 400 hours. A random sample of 64 of these light bulbs is taken.Referring to Scenario 7-3, what is the probability that the sample mean lifetime is more than 1,550 hours?

.8413

Given that X is a normally distributed variable with a mean of 50 and a standard deviation of 2, find the probability that X is between 47 and 54.

.9104

SCENARIO 7-5According to an article, 19% of the entire population in a developing country have high-speed access to the Internet. Random samples of size 200 are selected from the country's population.Referring to Scenario 7-5, the standard error of all the sample proportions is ________.

0.0277

The amount of time necessary for assembly line workers to complete a product is a normal variable with a mean of 15 minutes and a standard deviation of 2 minutes. The probability is ________ that a product is assembled in less than 20 minutes.

0.9938

If n = 10 and π = 0.70, then the standard deviation of the binomial distribution is

1.45.

The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound. If a sample of 25 fish yields a mean of 3.6 pounds, what is the Z-score for this observation?

2.500

The owner of a fish market determined that the average weight for a catfish is 3.2 pounds with a standard deviation of 0.8 pound. A citation catfish should be one of the top 2% in weight. Assuming the weights of catfish are normally distributed, at what weight (in pounds) should the citation designation be established?

4.84

SCENARIO 5-6The quality control manager of Green Bulbs Inc. is inspecting a batch of energy saving compact fluorescent light bulbs. When the production process is in control, the mean number of bad bulbs per shift is 6.0.Referring to Scenario 5-6, what is the probability that any particular shift being inspected has produced between 5.0 and 8.0 inclusive bad bulbs.

5622

The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound. What percentage of samples of 4 fish will have sample means between 3.0 and 4.0 pounds?

67%

If n = 10 and π = 0.70, then the mean of the binomial distribution is

7

Thirty-six of the staff of 80 teachers at a local intermediate school are certified in Cardio-Pulmonary Resuscitation (CPR). In 180 days of school, about how many days can we expect that the teacher on bus duty will likely be certified in CPR?

81 days

If a particular set of data is approximately normally distributed, we would find that approximately

All the above.

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a certain year in the past. Suppose a sample of 100 major league players was taken. Find the approximate probability that the mean salary of the 100 players exceeded $4.0 million.

Approximately 0

The local police department must write, on average, 5 tickets a day to keep department revenues at budgeted levels. Suppose the number of tickets written per day follows a Poisson distribution with a mean of 6.5 tickets per day. Interpret the value of the mean.

If we sampled all days, the arithmetic average or expected number of tickets written would be 6.5 tickets per day.

Which of the following about the normal distribution is not true?

It is a discrete probability distribution.

A professor receives, on average, 24.7 e-mails from students the day before the midterm exam. To compute the probability of receiving at least 10 e-mails on such a day, he will use what type of probability distribution?

Poisson distribution

On the average, 1.8 customers per minute arrive at any one of the checkout counters of a grocery store. What type of probability distribution can be used to find out the probability that there will be no customer arriving at a checkout counter?

Poisson distribution

Suppose a sample of n = 50 items is selected from a population of manufactured products and the weight, X, of each item is recorded. Prior experience has shown that the weight has a probability distribution with μ = 6 ounces and σ = 2.5 ounces. Which of the following is true about the sampling distribution of the sample mean if a sample of size 15 is selected?

The mean of the sampling distribution is 6 ounces.

SCENARIO 7-4According to a survey, only 15% of customers who visited the website of a major retail store made a purchase. Random samples of size 50 are selected.True or False: Referring to Scenario 7-4, the requirements for using a normal distribution to approximate a binomial distribution is fulfilled.

True

Whenever π = 0.5, the binomial distribution will

always be symmetric.

A probability distribution is an equation that

associates a particular probability of occurrence with each outcome.

A company has 125 personal computers. The probability that any one of them will require repair on a given day is 0.025. To find the probability that exactly 20 of the computers will require repair on a given day, one will use what type of probability distribution?

binomial distribution

What type of probability distribution will the consulting firm most likely employ to analyze the insurance claims in the following problem?An insurance company has called a consulting firm to determine if the company has an unusually high number of false insurance claims. It is known that the industry proportion for false claims is 3%. The consulting firm has decided to randomly and independently sample 100 of the company's insurance claims. They believe the number of these 100 that are false will yield the information the company desires.

binomial distribution

The Central Limit Theorem is important in statistics because

for a large n, it says the sampling distribution of the sample mean is approximately normal, regardless of the shape of the population.

If the expected value of a sample statistic is equal to the parameter it is estimating, then we call that sample statistic

unbiased