Stat Exam III Ch 5 & 6

Suppose that an airline uses a seat width of 16.7 in. Assume men have hip breadths that are normally distributed with a mean of 14.8 in. and a standard deviation of 1.1 in. If a plane is filled with 120 randomly selected​ men, find the probability that these men have a mean hip breadth greater than 16.7 in.

0.0000

In a​ state's Pick 3 lottery​ game, you pay $1.45 to select a sequence of three digits​ (from 0 to​ 9), such as 133. If you select the same sequence of three digits that are​ drawn, you win and collect ​$392.62. What is the probability of​ winning?

0.001

Based on a Comcast​ survey, there is a 0.8 probability that a randomly selected adult will watch​ prime-time TV​ live, instead of​ online, on​ DVR, etc. Assume that seven adults are randomly selected. Find the probability that fewer than three of the selected adults watch​ prime-time live.

0.00467

Suppose that an airline uses a seat width of 16.7 in. Assume men have hip breadths that are normally distributed with a mean of 14.8 in. and a standard deviation of 1.1 in. Find the probability that if an individual man is randomly​ selected, his hip breadth will be greater than 16.7 in.

0.0421

The following table describes the results of roadworthiness tests of Ford Focus cars that are three years old​ (based on data from the Department of​ Transportation). The random variable x represents the number of cars that failed among six that were tested for roadworthiness. Find the probability of getting three or more cars that fail among six cars tested. x P(x) 0 - 0.377 1 - 0.399 2 - 0.176 3 - 0.041 4 - 0.005 5 - 0+ 6 - 0+

0.046

If a procedure meets all of the conditions of a binomial distribution except the number of trials is not​ fixed, then the geometric distribution can be used. The probability of getting the first success on the xth trial is given by ​P(x)=p(1−p)x−1​, where p is the probability of success on any one trial. Subjects are randomly selected for a health survey. The probability that someone is a universal donor​ (with group O and type Rh negative​ blood) is 0.08. Find the probability that the first subject to be a universal blood donor is the seventh person selected.

0.0485.

If a procedure meets all of the conditions of a binomial distribution except the number of trials is not​ fixed, then the geometric distribution can be used. The probability of getting the first success on the xth trial is given by P(x)=p(1−p)x−1​, where p is the probability of success on any one trial. Subjects are randomly selected for a health survey. The probability that someone is a universal donor​ (with group O and type Rh negative​ blood) is 0.13. Find the probability that the first subject to be a universal blood donor is the sixth person selected.

0.0648

Assume that the red blood cell counts of women are normally distributed with a mean of 4.577 million cells per microliter and a standard deviation of 0.382 million cells per microliter. Approximately what percentage of women have red blood cell counts in the normal range from 4.2 to 5.4 million cells per​ microliter? Round to two decimal places.

82.26%

A common design requirement is that an environment must fit the range of people who fall between the 5th percentile for women and the 95th percentile for men. In designing an assembly work​ table, the sitting knee height must be​ considered, which is the distance from the bottom of the feet to the top of the knee. Males have sitting knee heights that are normally distributed with a mean of 21.5 in. and a standard deviation of 1.1 in. Females have sitting knee heights that are normally distributed with a mean of 19.3 in. and a standard deviation of 1.0 in. Use this information to answer the following questions. The author is writing this exercise at a table with a clearance of 23.2 in. above the floor. What percentage of men fit this​ table?

93.89%

Using the following uniform density​ curve, answer the question. A coordinate system has a horizontal x-axis labeled from 0 to 8 in increments of 1 and a vertical P(x)-axis labeled from 0 to 0.125 in increments of 0.125. A horizontal line segment extends from (0, 0.125) to (8, 0.125). A vertical line segment extends from (8, 0.125) to (8, 0). What is the probability that the random variable has a value greater than​ 5?

0.375

A​ bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If an applicant is randomly​ selected, find the probability of a rating that is between 200 and 275. Round to four decimal places.

0.4332

If z is a standard normal​ variable, find the probability that z lies between −2.41 and 0. Round to four decimal places.

0.4920

If z is a standard normal​ variable, find the probability that z lies between −2.41 and 0. Round to four decimal places.

0.4920

There is a 0.9984 probability that a randomly selected 27​-year-old male lives through the year. A life insurance company charges ​$199 for insuring that the male will live through the year. If the male does not survive the​ year, the policy pays out $100,000 as a death benefit. Can the insurance company expect to make a profit from many such​ policies? Why?

Yes, because the insurance company expects to make an average profit of ​$3939 on every 27-year-old male it insures for 1 year.

FIn a​ state's Pick 3 lottery​ game, you pay $1.45 to select a sequence of three digits​ (from 0 to​ 9), such as 133. If you select the same sequence of three digits that are​ drawn, you win and collect ​$392.62. Find the expected value.

$-1.06

There is a 0.9984 probability that a randomly selected 27​-year-old male lives through the year. A life insurance company charges ​$199 for insuring that the male will live through the year. If the male does not survive the​ year, the policy pays out $100,000 as a death benefit. If the 27​-year-old male purchases the​ policy, what is his expected​ value?

$-39

In a​ state's Pick 3 lottery​ game, you pay $1.45 to select a sequence of three digits​ (from 0 to​ 9), such as 133. If you select the same sequence of three digits that are​ drawn, you win and collect ​$392.62. If you​ win, what is your net​ profit?

$391.17

Assume that a randomly selected subject is given a bone density test. Bone density test scores are normally distributed with a mean of 0 and a standard deviation of 1. . This is the bone density score separating the bottom 12% from the top

-1.18

Assume that a randomly selected subject is given a bone density test. Bone density test scores are normally distributed with a mean of 0 and a standard deviation of 1. Draw a graph and find P5​, the 5th percentile. This is the bone density score separating the bottom 5% from the top 95%

-1.65

An elevator has a placard stating that the maximum capacity is 2430 lb—15 passengers.​ So, 15 adult male passengers can have a mean weight of up to 2430/15=162 pounds. If the elevator is loaded with 15 adult male​ passengers, find the probability that it is overloaded because they have a mean weight greater than 162 lb.​ (Assume that weights of males are normally distributed with a mean of 172 lb and a standard deviation of 34 lb​.)

0.8727

A study of the amount of time it takes a mechanic to rebuild the transmission for a 2010 Chevrolet Colorado shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly​ selected, find the probability that their mean rebuild time is less than 8.9 hours. Round to four decimal places.

0.9605

A common design requirement is that an environment must fit the range of people who fall between the 5th percentile for women and the 95th percentile for men. In designing an assembly work​ table, the sitting knee height must be​ considered, which is the distance from the bottom of the feet to the top of the knee. Males have sitting knee heights that are normally distributed with a mean of 21.5 in. and a standard deviation of 1.1 in. Females have sitting knee heights that are normally distributed with a mean of 19.3 in. and a standard deviation of 1.0 in. Use this information to answer the following questions. What percentage of women fit this​ table?

100.00%

In a​ state's Pick 3 lottery​ game, you pay $1.45 to select a sequence of three digits​ (from 0 to​ 9), such as 133. If you select the same sequence of three digits that are​ drawn, you win and collect ​$392.62. How many different selections are​ possible?

1000

Find the indicated critical value. Z0.01

2.33

A common design requirement is that an environment must fit the range of people who fall between the 5th percentile for women and the 95th percentile for men. In designing an assembly work​ table, the sitting knee height must be​ considered, which is the distance from the bottom of the feet to the top of the knee. Males have sitting knee heights that are normally distributed with a mean of 21.5 in. and a standard deviation of 1.1 in. Females have sitting knee heights that are normally distributed with a mean of 19.3 in. and a standard deviation of 1.0 in. Use this information to answer the following questions. What is the minimum table clearance required to satisfy the requirement of fitting​ 95% of​ men?

23.3

A common design requirement is that an environment must fit the range of people who fall between the 5th percentile for women and the 95th percentile for men. In designing an assembly work​ table, the sitting knee height must be​ considered, which is the distance from the bottom of the feet to the top of the knee. Males have sitting knee heights that are normally distributed with a mean of 21.4 in. and a standard deviation of 1.3 in. Females have sitting knee heights that are normally distributed with a mean of 19.4 in. and a standard deviation of 1.2 in. What is the minimum table clearance required to satisfy the requirement of fitting​ 95% of​ men?

23.5 in

On a multiple choice test with 17​ questions, each question has four possible​ answers, one of which is correct. For students who guess at all​ answers, find the mean for the number of correct answers. Round to the nearest tenth as needed.

4.3 questions

Assume that the red blood cell counts of women are normally distributed with a mean of 4.577 million cells per microliter and a standard deviation of 0.382 million cells per microliter. Find the 80th percentile for the red blood cell counts of women. Round to three decimal places.

4.898 million cells per microliter

A common design requirement is that an environment must fit the range of people who fall between the 5th percentile for women and the 95th percentile for men. In designing an assembly work​ table, the sitting knee height must be​ considered, which is the distance from the bottom of the feet to the top of the knee. Males have sitting knee heights that are normally distributed with a mean of 21.4 in. and a standard deviation of 1.3 in. Females have sitting knee heights that are normally distributed with a mean of 19.4 in. and a standard deviation of 1.2 in. The author is writing this exercise at a table with a clearance of 23.6 in. above the floor. What percentage of men fit this​ table?

95.47%

A common design requirement is that an environment must fit the range of people who fall between the 5th percentile for women and the 95th percentile for men. In designing an assembly work​ table, the sitting knee height must be​ considered, which is the distance from the bottom of the feet to the top of the knee. Males have sitting knee heights that are normally distributed with a mean of 21.4 in. and a standard deviation of 1.3 in. Females have sitting knee heights that are normally distributed with a mean of 19.4 in. and a standard deviation of 1.2 in. What percentage of women fit this​ table?

99.98%

Find the indicated area under the curve of the standard normal​ distribution; then convert it to a percentage and fill in the blank. About​ ______% of the area is between z=−1 and z=1 ​(or within 1 standard deviation of the​ mean).

About 68.27 of the area is between z=−1 and z=1 ​(or within 1 standard deviation of the​ mean).

Identify the given random variable as being discrete or continuous. The cost of a randomly selected orange

Discrete

An unbiased estimator is a statistic that targets the value of the of the population parameter such that the sampling distribution of the statistic has a​ ________ equal to the​ ________ of the corresponding parameter.`

Mean; mean

In a​ state's Pick 3 lottery​ game, you pay $1.45 to select a sequence of three digits​ (from 0 to​ 9), such as 133. If you select the same sequence of three digits that are​ drawn, you win and collect ​$392.62. If you bet $1.45 in a certain​ state's Pick 4​ game, the expected value is −$1.06. Which bet is​ better, a ​$1.45 bet in the Pick 3 game or a $1.45 bet in the Pick 4​ game? Explain.

Neither bet is better because both games have the same expected value.

The Acme Candy Company claims that​ 60% of the jawbreakers it produces weigh more than 0.4 ounces. Suppose that 800 jawbreakers are selected at random from the production lines. Would it be significant for this sample of 800 to contain 494 jawbreakers that weigh more than 0.4​ ounces? Consider as significant any result that differs from the mean by at least 2 standard deviations. That​ is, significant values are either less than or equal to μ−2σ or greater than or equal to μ+2σ.

No

An elevator has a placard stating that the maximum capacity is 2430 lb—15 passengers.​ So, 15 adult male passengers can have a mean weight of up to 2430/15=162 pounds. Does this elevator appear to be​ safe?

No, there is a good chance that 15 randomly selected adult male passengers will exceed the elevator capacity.

Weights of golden retriever dogs are normally distributed. Samples of weights of golden retriever​ dogs, each of size n=​15, are randomly collected and the sample means are found. Is it correct to conclude that the sample means cannot be treated as being from a normal distribution because the sample size is too​ small? Explain.

No; the original population is normally​ distributed, so the sample means will be normally distributed for any sample size.

Determine whether the given procedure results in a binomial distribution. If​ not, state the reason why. Rolling a single die 26​ times, keeping track of the numbers that are rolled

Not​ binomial: there are more than two outcomes for each trial.

Three randomly selected households are surveyed. The numbers of people in the households are 3​, 4​, and 11. Assume that samples of size n=2 are randomly selected with replacement from the population of 3​, 4​, and 11. Sample x1 x2 1 3 3 2 3 4 3 3 11 4 4 3 5 4 4 6 4 11 7 11 3 8 11 4 9 11 11 Construct a probability distribution table that describes the sampling distribution of the proportion of odd numbers when samples of sizes n=2 are randomly selected.

Sample proportion vs probability 0 - 1/9 0.5 - 4/9 1 - 4/9

Three randomly selected households are surveyed. The numbers of people in the households are 2​, 4​, and 12. Assume that samples of size n=2 are randomly selected with replacement from the population of 2​, 4​, and 12. Listed below are the nine different samples. Sample x1 x2 1 2 2 2 2 4 3 2 12 4 4 2 5 4 4 6 4 12 7 12 2 8 12 4 9 12 12 Compare the population variance to the mean of the sample variances. Choose the correct answer below.

The population variance is equal to the mean of the sample variances.

Determine whether the given procedure results in a binomial distribution. If​ not, state the reason why. Rolling a single die 53​ times, keeping track of the​ "fives" rolled.

The procedure results in a binomial distribution.

Three randomly selected households are surveyed. The numbers of people in the households are 3​, 4​, and 11. Assume that samples of size n=2 are randomly selected with replacement from the population of 3​, 4​, and 11. Sample x1 x2 1 3 3 2 3 4 3 3 11 4 4 3 5 4 4 6 4 11 7 11 3 8 11 4 9 11 11 Does the mean of the sample proportions equal the proportion of odd numbers in the​ population?

The proportion of odd numbers in the population is equal to the mean of the sample proportions.

If a plane is filled with 120 randomly selected​ men, find the probability that these men have a mean hip breadth greater than 16.7 in.

The result from part (a) the seats are occupied by individuals rather than means.

Suppose that an airline uses a seat width of 16.7 in. Assume men have hip breadths that are normally distributed with a mean of 14.8 in. and a standard deviation of 1.1 in. Which result should be considered for any changes in seat​ design: the result from part​ (a) or part​ (b)?

The result from part (a) should be considered because the seats are occupied by individuals rather than means.

Three randomly selected households are surveyed. The numbers of people in the households are 3​, 4​, and 11. Assume that samples of size n=2 are randomly selected with replacement from the population of 3​, 4​, and 11. Sample x1 x2 1 3 3 2 3 4 3 3 11 4 4 3 5 4 4 6 4 11 7 11 3 8 11 4 9 11 11 Do the sample proportions target the value of the population​ proportion? Does the sample proportion make a good estimator of the population​ proportion?

The sample proportions target the proportion of odd numbers in the​ population, so sample proportions make good estimators of the population proportion.

Three randomly selected households are surveyed. The numbers of people in the households are 2​, 4​, and 12. Assume that samples of size n=2 are randomly selected with replacement from the population of 2​, 4​, and 12. Listed below are the nine different samples. Sample x1 x2 1 2 2 2 2 4 3 2 12 4 4 2 5 4 4 6 4 12 7 12 2 8 12 4 9 12 12 Do the sample variances target the value of the population​ variance? In​ general, do sample variances make good estimators of population​ variances? Why or why​ not?

The sample variances target the population​ variances, therefore, sample variances make good estimators of population variances.

A common design requirement is that an environment must fit the range of people who fall between the 5th percentile for women and the 95th percentile for men. In designing an assembly work​ table, the sitting knee height must be​ considered, which is the distance from the bottom of the feet to the top of the knee. Males have sitting knee heights that are normally distributed with a mean of 21.5 in. and a standard deviation of 1.1 in. Females have sitting knee heights that are normally distributed with a mean of 19.3 in. and a standard deviation of 1.0 in. Use this information to answer the following questions. Determine if the following statement is true or false. If there is clearance for​ 95% of​ males, there will certainly be clearance for all women in the bottom​ 5%.

The statement is true because the 95th percentile for men is greater than the 5th percentile for women.

A common design requirement is that an environment must fit the range of people who fall between the 5th percentile for women and the 95th percentile for men. In designing an assembly work​ table, the sitting knee height must be​ considered, which is the distance from the bottom of the feet to the top of the knee. Males have sitting knee heights that are normally distributed with a mean of 21.4 in. and a standard deviation of 1.3 in. Females have sitting knee heights that are normally distributed with a mean of 19.4 in. and a standard deviation of 1.2 in. Determine if the following statement is true or false. If there is clearance for​ 95% of​ males, there will certainly be clearance for all women in the bottom​ 5%.

The statement is true because the 95th percentile for men is greater than the 5th percentile for women.

A common design requirement is that an environment must fit the range of people who fall between the 5th percentile for women and the 95th percentile for men. In designing an assembly work​ table, the sitting knee height must be​ considered, which is the distance from the bottom of the feet to the top of the knee. Males have sitting knee heights that are normally distributed with a mean of 21.4 in. and a standard deviation of 1.3 in. Females have sitting knee heights that are normally distributed with a mean of 19.4 in. and a standard deviation of 1.2 in. Does the table appear to be made to fit almost​ everyone? Choose the correct answer below.

The table will fit almost everyone except about 5​% of men with the largest sitting knee heights.

A common design requirement is that an environment must fit the range of people who fall between the 5th percentile for women and the 95th percentile for men. In designing an assembly work​ table, the sitting knee height must be​ considered, which is the distance from the bottom of the feet to the top of the knee. Males have sitting knee heights that are normally distributed with a mean of 21.5 in. and a standard deviation of 1.1 in. Females have sitting knee heights that are normally distributed with a mean of 19.3 in. and a standard deviation of 1.0 in. Use this information to answer the following questions. Does the table appear to be made to fit almost​ everyone? Choose the correct answer below.

The table will fit almost everyone except about 6​% of men with the largest sitting knee heights.

When conducting research on color blindness in​ males, a researcher forms random groups with five males in each group. The random variable x is the number of males in the group who have a form of color blindness. Determine whether a probability distribution is given. If a probability distribution is​ given, find its mean and standard deviation. If a probability distribution is not​ given, identify the requirements that are not satisfied x P(x) 0 0.668 1 0.276 2 0.051 3 0.004 4 0.001 5 0.000 Does the table show a probability​ distribution?

Yes, the table shows a probability distribution.

Identify the given random variable as being discrete or continuous. The braking time of a car

continuous

An unbiased estimator is a statistic that targets the value of the of the population parameter such that the sampling distribution of the statistic has a​ ________ equal to the​ ________ of the corresponding parameter.

mean; mean

Three randomly selected households are surveyed. The numbers of people in the households are 2​, 4​, and 12. Assume that samples of size n=2 are randomly selected with replacement from the population of 2​, 4​, and 12. Listed below are the nine different samples. Sample x1 x2 1 2 2 2 2 4 3 2 12 4 4 2 5 4 4 6 4 12 7 12 2 8 12 4 9 12 12 Find the variance of each of the nine​ samples, then summarize the sampling distribution of the variances in the format of a table representing the probability distribution of the distinct variance values.

s^2 probability 0 - 1/3 2 - 2/9 32 - 2/9 50 - 2/9

There is a 0.9984 probability that a randomly selected 27​-year-old male lives through the year. A life insurance company charges ​$199 for insuring that the male will live through the year. If the male does not survive the​ year, the policy pays out $100,000 as a death benefit. From the perspective of the 27​-year-old ​male, what are the monetary values corresponding to the two events of surviving the year and not​ surviving?

surviving the year: $-199 not surviving: $99801

When conducting research on color blindness in​ males, a researcher forms random groups with five males in each group. The random variable x is the number of males in the group who have a form of color blindness. Determine whether a probability distribution is given. If a probability distribution is​ given, find its mean and standard deviation. If a probability distribution is not​ given, identify the requirements that are not satisfied x P(x) 0 0.668 1 0.276 2 0.051 3 0.004 4 0.001 5 0.000 Find the mean of the random variable x. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

μ=0.4

Groups of adults are randomly selected and arranged in groups of three. The random variable x is the number in the group who say that they would feel comfortable in a​ self-driving vehicle. Determine whether a probability distribution is given. If a probability distribution is​ given, find its mean and standard deviation. If a probability distribution is not​ given, identify the requirements that are not satisfied. x P(x) 0 0.359 1 0.445 2 0.175 3 0.021 Find the mean of the random variable x. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice

μ=0.9​

When conducting research on color blindness in​ males, a researcher forms random groups with five males in each group. The random variable x is the number of males in the group who have a form of color blindness. Determine whether a probability distribution is given. If a probability distribution is​ given, find its mean and standard deviation. If a probability distribution is not​ given, identify the requirements that are not satisfied x P(x) 0 0.668 1 0.276 2 0.051 3 0.004 4 0.001 5 0.000 Find the standard deviation of the random variable x. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

σ=0.6

Groups of adults are randomly selected and arranged in groups of three. The random variable x is the number in the group who say that they would feel comfortable in a​ self-driving vehicle. Determine whether a probability distribution is given. If a probability distribution is​ given, find its mean and standard deviation. If a probability distribution is not​ given, identify the requirements that are not satisfied. x P(x) 0 0.359 1 0.445 2 0.175 3 0.021 Find the standard deviation of the random variable x. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

σ=0.8

Use the given values of n=93 and p=0.24 to find the maximum value that is significantly​ low, μ−2σ​, and the minimum value that is significantly​ high, μ+2σ. Round your answer to the nearest hundredth unless otherwise noted.

​Minimum: 14.08 ​Maximum: 30.56

Groups of adults are randomly selected and arranged in groups of three. The random variable x is the number in the group who say that they would feel comfortable in a​ self-driving vehicle. Determine whether a probability distribution is given. If a probability distribution is​ given, find its mean and standard deviation. If a probability distribution is not​ given, identify the requirements that are not satisfied. x P(x) 0 0.359 1 0.445 2 0.175 3 0.021 Does the table show a probability​ distribution?

​Yes, the table shows a probability distribution.