Question 1

A random sample of 75 light bulbs is drawn from a population with mean $$\mu = 15,000$$ hours and standard deviation $$\sigma = 350$$ hours. What is the probability that the sample mean is less than 14,900 hours? Use the Central Limit Theorem and round your answer to four decimal places.

Accepted Answer

$$0.0062$$

Question 2

Given a normal distribution with mean $$\mu = 15,000$$ and standard deviation $$\sigma = 40$$, what is $$P(x \leq 15,025)$$?

Accepted Answer

$$0.7340$$

Question 3

For a normal distribution with mean $$\mu = 15,000$$ and standard deviation $$\sigma = 40$$, what is the probability that $$x \geq 14,975$$?

Accepted Answer

$$0.7340$$

Question 4

A sample of 75 light bulbs has a mean time to failure of $$15,000$$ hours and a standard deviation of $$40$$ hours. What is the probability that the sample mean is greater than $$15,105$$ hours?

Accepted Answer

$$0.0043$$

Question 5

For a normal distribution with mean $$\mu = 15,000$$ and standard deviation $$\sigma = 40$$, what is the probability that $$14,950 \leq x \leq 15,050$$?

Accepted Answer

$$0.7887$$

Question 6

For a normal distribution with mean $$\mu = 15,000$$ and standard deviation $$\sigma = 40$$, what is the probability that $$14,960 \leq x \leq 15,010$$?

Accepted Answer

$$0.4400$$

Question 7

For a normal distribution with mean $$\mu = 15,000$$ and standard deviation $$\sigma = 40$$, which value corresponds to the 80th percentile?

Accepted Answer

$$15,033.665$$

Question 8

For a normal distribution with mean $$\mu = 15,000$$ and standard deviation $$\sigma = 40$$, 40% of all possible sample means are less than which value?

Accepted Answer

$$14,989.866$$

Question 9

According to the 2024 AVMA Pet Ownership and Demographic Sourcebook, 32.1% of US households own a cat. If we randomly select 1024 households, what is the probability that the sample proportion is less than 33%?

Accepted Answer

$$0.7312$$

Question 10

For a sample proportion with mean $$0.321$$ and standard deviation $$0.0146$$, what is the probability that the sample proportion is less than $$0.3$$?

Accepted Answer

$$0.0752$$

Question 11

For a sample proportion with mean $$0.321$$ and standard deviation $$0.0146$$, what is the probability that the sample proportion is greater than $$0.305$$?

Accepted Answer

$$0.8634$$

Question 12

For a sample proportion with mean $$0.321$$ and standard deviation $$0.0146$$, what is the probability that the sample proportion is greater than $$0.335$$?

Accepted Answer

$$0.1688$$

Question 13

For a sample proportion with mean $$0.321$$ and standard deviation $$0.0146$$, what is the probability that $$0.295 \leq p \leq 0.3175$$?

Accepted Answer

$$0.3678$$

Question 14

For a sample proportion with mean $$0.321$$ and standard deviation $$0.0146$$, what is the probability that $$0.3025 \leq p \leq 0.3325$$?

Accepted Answer

$$0.6819$$

Question 15

For a sample proportion with mean $$0.321$$ and standard deviation $$0.0146$$, which value corresponds to the 25th percentile?

Accepted Answer

$$0.3112$$

Question 16

For a sample proportion with mean $$0.321$$ and standard deviation $$0.0146$$, 60% of all possible sample proportions are less than what value?

Accepted Answer

$$0.3247$$

Question 17

A survey of 175 high school students found that 137 participate in extracurricular activities. What is the 95% confidence interval for the proportion of students who participate?

Accepted Answer

$$0.7218 to$$ $$0.8442$$

Question 18

The Texas Department of Agriculture collected weights from 10 pecan trees. The sample mean was $$118$$ pounds, and the standard error was $$6.34. $$What is the 90% confidence interval for the mean weight?

Accepted Answer

$$106.39 to$$ $$129.61$$

Question 19

In a sample of 85 people, 48 plan to return to Wally World within 6 months. What is the 99% confidence interval for the proportion of visitors who plan to return?

Accepted Answer

$$0.4262 to$$ $$0.7032$$

Question 20

A local vet believes the percentage of households owning a cat in his county is higher than the national average of 32.1%. In a sample of 146 households, 50 own a cat. What is the P-value for this hypothesis test?

Accepted Answer

$$0.2893$$

Step-by-Step Guidance for Probability and Confidence Interval Questions (Statistics)

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