Question 1

A population of 6-week-old potato plants has weights that are normally distributed with a mean of 9.1 pounds and a standard deviation of 2.4 pounds. What is the 13th percentile of the weights?

Accepted Answer

$$7.47$$

Question 2

For a particular diamond mine, 76% of the diamonds fail to qualify as 'gemstone grade.' If a random sample of 96 diamonds is analyzed, what is the mean number of diamonds that fail to qualify?

Accepted Answer

$$72.96$$

Question 3

For a particular diamond mine, 76% of the diamonds fail to qualify as 'gemstone grade.' A random sample of 113 diamonds is analyzed. What is the standard deviation of the number of diamonds that fail to qualify?

Accepted Answer

$$4.47$$

Question 4

In a diamond mine, 77% of the diamonds fail to qualify as 'gemstone grade.' In a random sample of 121 diamonds, what is the probability that more than 81% of the sample fail to qualify? (Use normal approximation.)

Accepted Answer

$$0.1211$$

Question 5

A cat breeder recently found that 87% of the giant Japanese pons (imported cats) in a sample of 162 were long-haired. What is the probability that less than 80% of the sample are long-haired pons (using normal approximation)?

Accepted Answer

$$0.0133$$

Question 6

A survey of 847 registered voters found that 157 of them wished to see Mayor Wolffelrake lose her next election. The Wolffelrake campaign claims that no more than 21% of registered voters wish to see her defeated. Does the 90% confidence interval for the proportion support this claim? (The 90% confidence interval is (0.172, 0.204).)

Accepted Answer

Yes

Question 7

A garden supplier claims that its new variety of giant tomato produces fruit with a mean weight of 44 ounces. A test is made of $$H_0$$: \mu = 44$$ versus H_1$: \mu 
eq 44. $$The null hypothesis is not rejected. What is the appropriate conclusion?

Accepted Answer

There is not enough evidence to conclude that the mean weight differs from 44 ounces.

Question 8

Which of the following best describes the shape of a normal distribution?

Accepted Answer

Symmetrical and bell-shaped

Question 9

A researcher collects data on the number of hours students spend on homework per week and finds the data to be approximately normally distributed with a mean of 15 hours and a standard deviation of 3 hours. What percentage of students spend between 12 and 18 hours on homework per week?

Accepted Answer

$$68\%$$

Question 10

A table shows the following data for gender and eye color in a sample: 24 males with green eyes, 18 females with green eyes, 31 males with other eye colors, and 27 females with other eye colors. What is the probability that a randomly selected individual is female given that the individual has green eyes?

Accepted Answer

$$\frac{18}{42}$$

Question 11

A teacher records the following data for students' preferred study methods: 47 prefer homework, 12 prefer homework+experiments, 39 prefer experiments, 32 prefer other methods, and 11 prefer both homework and experiments. What is the probability that a randomly selected student prefers either homework or experiments (but not both)?

Accepted Answer

$$\frac{47+39}{141}$$

Question 12

If $$X is a $$normally distributed random variable with mean $$\mu = 100$$ and standard deviation $$\sigma = 15$$, what is the $$z-$$score for $$X = 130$$?

Accepted Answer

$$2.0$$

Question 13

Which of the following statements about confidence intervals is correct?

Accepted Answer

A 95% confidence interval means that if we repeated the sampling process many times, about 95% of the intervals would contain the true parameter.

Question 14

A sample of 50 batteries has a mean life of 500 hours and a standard deviation of 20 hours. What is the 95% confidence interval for the mean battery life?

Accepted Answer

$$500 \pm 5.54$$

Question 15

Which of the following is NOT an assumption for using the normal approximation to the binomial distribution?

Accepted Answer

The sample size is small.

Question 16

A researcher wants to test if a new fertilizer increases the mean yield of a crop above 50 kg per plot. Which is the correct null hypothesis?

Accepted Answer

$$H_0$$: \mu = 50$$

Question 17

If the $$p-$$value for a hypothesis test is 0.03 and the significance level is 0.05, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis.

Question 18

Which of the following best describes a Type I error in hypothesis testing?

Accepted Answer

Rejecting a true null hypothesis.

Question 19

A normal distribution has mean $$\mu = 0$$ and standard deviation $$\sigma = 1. $$What is the probability that a randomly selected value is between $$-1$$ and $$1$$?

Accepted Answer

$$0.68$$

Core Concepts in College Statistics: Probability, Normal Models, Hypothesis Testing, and Categorical Data

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