# mathematics

13.

For which of the following situations would the histogram of the sample mean (sampling distribution) NOT be normally distributed (follow a normal curve)?

A) A random sample of size 20 is drawn from a skewed population.

B) A random sample of size 50 is drawn from a skewed population.

C) A random sample of size 20 is drawn from a normally distributed population.

D) A random sample of size 50 is drawn from a normally distributed population.

Histograms of sample statistic values (i.e. sampling distributions) will be centered at the population value (µ or p) and will have an average spread around the population value that is measured by the standard deviation of the sampling distribution.

The Standard Deviation of our sampling distribution

= formula for a sampling distribution for sample means (where σ is the population standard deviation and n is the sample size)

= formula for a sampling distribution for sample proportions (where p is the population proportion and n is the sample size)

14.

We are given that the average amount spent on textbooks by all incoming freshmen was \$400 (μ) with a standard deviation of \$25 (σ). The sampling distribution of the sample mean for randomly selected samples of 100 freshmen has a standard deviation of \$2.50. Which of the following is the correct interpretation of the population standard deviation compared to the sampling distribution’s standard deviation?

A) The population standard deviation of \$25 gives the variation in amount spent amongst all freshmen. The sampling distribution’s standard deviation of \$2.50 gives the variation in the average amount spent amongst all samples of 100 freshmen.

B) The population standard deviation of \$25 gives the variation in the average amount spent amongst all samples of 100 freshmen. The sampling distribution’s standard deviation of \$2.50 gives the variation in amount spent amongst all freshmen.

15.

Forty percent (40% or 0.40, as a proportion) of all cars owned by residents of Lordstown, OH and the surrounding area are the Chevrolet brand. If a random sample of 81 car owners is selected in that area, then the sampling distribution of the sample proportion of those who own a Chevrolet brand car will be centered around 0.40 (40%) with a standard deviation of:

A) .09 or 9%

B) .054 or 5.4%

C) .946 or 94.6%

D) .044 or 4.4%

16.

A kitchen cabinet business has primarily homeowners as customers, but also has a few customers that are developers who build multi-unit condominiums. Overall, the average sale is \$15,000, with a median sale of \$10,000 and a standard deviation of \$4,800. The standard deviation of the averages for samples of 100 customers would be which of the following? In other words, what is the standard deviation of the sampling distribution of the sample means from samples of 100 customers?

A) \$4,800

B) \$480

C) \$48

D) \$4.80

If the sampling distribution is normally distributed, we can use the Standard Normal Table (Table 8.1) to compute the probabilities of certain intervals of sample statistic values. We calculate the Z score using a formula given below that uses the standard deviation of the sampling distribution in the denominator and that uses the observed sample statistic and population parameter in the numerator.

17.

Twenty percent (20%) of all students who live on campus at Penn State’s University Park campus have a car that they have registered to park in one of the University’s parking lots. You randomly select 100 students who live on campus and find that 24 of the 100 have a car registered to park in one of the University’s parking lots. What is the standard score (i.e. Z score) of your sample proportion?

A) +.24

B) + 1.00

C) -1.00

D) + .20

18.

Twenty percent (20%) of all students who live on campus at Penn State’s University Park campus have a car that they have registered to park in one of the University’s parking lots. You randomly select 100 students who live on campus and find that 18 of the 100 have a car registered to park in one of the University’s parking lots. A sample proportion of 0.18 has a standard score (Z score) of -0.50. What is the probability of having a sample proportion less than 0.18? Use Table 8.1.

A) 69%

B) 31%

C) 50%

D) 95%

19.

The average monthly cell phone bill for all customers of a particular cell phone carrier in Pennsylvania is \$85 with a standard deviation of \$10. What is the standard score (Z score) for a random sample of 25 customers with an average amount spent monthly of \$90?

A) +.50

B) – .50

C) +2.5

D) -2.5

20.

The average monthly cell phone bill for all customers of a particular cell phone carrier in Pennsylvania is \$85 with a standard deviation of \$10. For a sample size of 25, a sample mean of \$87 has a Z score of +1.00, and a sample mean of \$83 has a Z score of -1.00. We want to know the probability of obtaining a sample of size 25 that has a sample mean between \$83 and \$87. To find this we must find the probability of obtaining a Z score between -1 and +1. What is this probability?

A) 90%

B) 95%

C) 68%

D) none of the above

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