AP Stats 7.3 Quiz

A manufacture claims that only 2% of their products are defective. A store takes delivery of 300 items from the manufacture. Let X = the number of defective items. Assuming the manufacture is correct that only 2% of their products are defective, what are the mean and standard deviation of the sampling distribution of X?

• The mean number of defective items is 6 and the standard deviation is 5.88.

• The mean number of defective items is 6 and the standard deviation is 2.42.

• The mean number of defective items is 2 and the standard deviation is 5.88.

• The mean number of defective items is 2 and the standard deviation is 2.42

Answer explanation

Make sure to look at section 7.3 notes

Ninety percent of the students at a high school are right-handed. Which of the following sample sizes is the smallest that satisfies the large count condition to approximate the distribution as a normal distribution?

• 25

• 50

• 85

• 120

A random sample of 120 students at a certain high school was asked if they spend more than 4 hours a night on homework. Assume the true proportion of students that spend more than 4 hours a night on homework is 15%, which of the following is closest to the probability that more than 20% of the students in a sample would respond that they spend more than 4 hours a night on homework?

• 0.0625

• 0.0809

• 0.9191

• 0.9375

The distribution of the number of siblings students at a local high school have has a mean of 2.2 siblings and a standard deviation of 1.4 siblings. Suppose we select a random sample of 40 students at the high school. 

Let "x-bar" = the sample mean number of siblings for students in your sample. What is the standard deviation of the sampling distribution of "x-bar"and what does it mean? 

• In SRSs of size 40 from the high school, the sample mean number of siblings in the sample would typically vary by about 6.32 from the true average of 2.2 siblings.

• In SRSs of size 40 from the high school, the sample mean number of siblings in the sample would typically vary by about 1.4 from the true average of 2.2 siblings.

• In SRSs of size 40 from the high school, the sample mean number of siblings in the sample would typically vary by about 0.22 from the true average of 2.2 siblings.

• In SRSs of size 40 from the high school, the sample mean number of siblings in the sample would typically vary by about 0.035 from the true average of 2.2 siblings.

Answer explanation

"x-bar" means:  $\overline{x}$  

A sample of size n = 100 was taken from the residents in a large city to estimate the average number pets the residences own. The sample mean, "x-bar" , was 1.91 pets. Suppose m, the true mean number of pets owned by residents in the city, is 1.75 pets with a standard deviation, s, of 1.1 pets. What is the mean and the standard deviation of the sampling distribution of "x-bar"?

• The mean is 1.91 pets and the standard deviation is 1.1 pets.

• The mean is 1.91 pets and the standard deviation is 0.11 pets.

• The mean is 1.75 pets and the standard deviation is 0.11 pets.

• The mean is 1.75 pets and the standard deviation is 0.011 pets.

Answer explanation

Note that "x-bar" means: $\overline{x}$

A company produces tortillas that are supposed to have an average diameter of 6 inches. Each of the tortillas the machine produces is slightly different, but the distribution diameters is approximately normal with a mean of 6.05 inches and a standard deviation of 0.2 inches. A bag that contains 10 tortillas claims the diameter of the tortillas in the bag is 6 inches. Suppose the 10 tortillas in the bag represent a random selection of all tortillas produced by the machine. What is the approximate probability that the mean diameter of the 10 tortillas in the bag is less than the claim of 6 inches?

• 0.0062

• 0.2146

• 0.7854

• 0.4013

The heights of the players on high school basketball teams in a certain state are approximately normally distributed with a mean of 73 inches and a standard deviation of 3.75 inches. Consider the local high school team to be a random selection of 11 players from the state. What is the approximate probability the 11 players on a team will have a mean height of less than 72 inches?

• 0.3949

• 0.1882

• 0.0434

• 0.0017

A sample of size n will to be taken from the residences in a large city to estimate the mean price of their home. The distribution of home values in the city is strongly skewed right. Which of the following is the smallest sample size such that the sampling distribution of is approximately normal?

• Since the population is strongly skewed right, no sample size will have a sampling distribution that is approximately normal.

• A sample of size 10 is the smallest sample size that will have a sampling distribution that is approximately normal.

• A sample of size 30 is the smallest sample size that will have a sampling distribution that is approximately normal.

• The central limit theorem guarantees that all samples of size n will have a sampling distribution that is approximately normal.

Scores on the mathematics part of the SAT exam in a recent year were roughly Normal with mean 515 and standard deviation 114. You choose an SRS of 100 students and average their SAT Math scores. Suppose that you do this many, many times. Which of the following are the mean and standard deviation of the sampling distribution of

• Mean = 515, SD = $\frac{114}{\sqrt{100}}$

• Mean = 515, SD = 114

• Mean = 515/100, SD = 114/100

• Mean = 515/100, SD = $\frac{114}{\sqrt{100}}$

The number of hours a lightbulb burns before failing varies from bulb to bulb. The population distribution of burnout times is strongly skewed to the right. The central limit theorem says that

• as we look at more and more bulbs, their average burnout time gets ever closer to the mean μ for all bulbs of this type.

• the average burnout time of a large number of bulbs has a sampling distribution with the same shape (strongly skewed) as the population distribution.

• the average burnout time of a large number of bulbs has a sampling distribution that is exactly Normal.

• the average burnout time of a large number of bulbs has a sampling distribution that is close to Normal.