1. According to Central Limit theorem, which sample size will give a smaller
standard error of the mean?
A. 7 B. 12 C. 23 D. 40
2. If a population is not normally distributed, the distribution of the sample means
for a given sample size n will ____________.
A. be positively skewed.
B. be negatively skewed.
C. take the same shape as the population.
D. approach a normal distribution as n increases.
3. The mean and standard deviation of a population are 75 and 15, respectively.
The sample size is 100. What is the standard error of the mean?
A. 1.5 B. 1.73 C. 0.15 D. 8
4. The mean and standard deviation of a population are 400 and 40, respectively.
Sample size is 25. What is the mean of the sampling distribution?
A. 400 B. 40 C. 25 D. 8
5. What is the standard error of the mean if the sample size is 25 with standard
deviation of 16?
A. 6.25 B. 3.2 C. 1.25 D. 0.64
6. The weights of the eggs produced by a certain breed of hen are normally
distributed with mean 65 grams and standard deviation of 5 grams. Which of
the following will you use?
A. Normal Distribution C. Discrete Probability Distribution
B. Central Limit Theorem D. Binomial Distribution
7. In a study done on the life expectancy of 500 people in a certain geographic region,
the mean age at death was 72 years and the standard deviation was 5.3 years.
If a sample of 50 people from this region is selected, and the probability that the
mean life expectancy will be less than 70 years, which of the following will you
use?
A. Normal Distribution C. Discrete Probability Distribution
B. Central Limit Theorem D. Binomial Distribution
16
8. The mean and standard deviation of a population are 200 and 20,
respectively. What is the probability of selecting 25 data values with a mean less
than 190?
A. 69% B. 31% C. 0.6% D. 99%
9. In a metal fabrication process, metal rods are produced that have an average
length of 20.5 meters with a standard deviation of 2.3 meters. A quality control
specialist collects a random sample of 30 rods and measures their lengths.
Suppose the resulting sample mean is 19.5 meters. Which of the following
statements is true?
A. This sample mean is 2.38 standard deviations above what we expect.
B. This sample mean is 2.38 standard deviations below what we expect.
C. This sample mean is only 1 standard deviation above the population mean.
D. This sample mean is more than 3 standard deviations away from the
population mean.
For number 10-11, refer to the problem below.
Suppose the teenagers that attend public high schools get an average of 5.7
hours of sleep each night with a standard deviation of 1.7 hours. Assume that
the average sleep hour is normally distributed, and 35 high school students are
randomly selected.
10.Compute the z-score for 6 hours of sleep.
A. 1.04 B. 0.18 C. 0.52 D. 0.82
11.What is the probability that a randomly selected group of 35 high school
students gets more than 6 hours of sleep each night?
A. 0.3508 B. 0.1492 C. 0.0714 D. 0.4286
For number 12-14, refer to the problem below.
The amount of fuel used by jumbo jets to take off is normally distributed with
a mean of 4, 000 gallons and a standard deviation of 125 gallons. A sample of 40
jumbo jets are randomly selected.
12.Compute the z-score for 3, 950 gallons.
A. – 0.4 B. 0.4 C. – 2.53 D. 2.53
13.What is the probability that the mean number of gallons of fuel needed to take off
for a randomly selected sample of 40 jumbo jets will be less than 3, 950 gallons?
a. 78.1% B. 34.5% C. 2.5% D. 0.57%
14.What is the probability that the mean number of gallons of fuel needed to take off
for a randomly selected sample of 40 jumbo jets will be more than 3, 950 gallons?
b. 0.57% B. 49.43% C. 65.54% D. 99.43%
15.Researchers found that boys playing high school football recorded an average of
355 hits to the head with a standard deviation of 80 hits during a season. What
is the probability on a randomly selected team of 48 players that the average
number of head hits per player is between 340 and 360?
A. 56.96% B. 43.04% C. 40.32% D. 16.64%