Question 1

Given the following probability distribution for the number of defective computers in a batch of 4: $$P(0) = 0.6561$$, $$P(1) = 0.2916$$, $$P(2) = 0.0486$$, $$P(3) = 0.0036$$, $$P(4) = 0.0001$$, what is the mean number of defective computers per batch? Round your answer to the nearest tenth.

Accepted Answer

$$0.4$$

Question 2

For the probability distribution $$x: 0,1,2,3,4$$ with $$P(x): 0.19, 0.41, 0.21, 0.07, 0.12$$, what is the standard deviation? Round to the nearest hundredth.

Accepted Answer

$$1.53$$

Question 3

You pay $$3.00 to roll a fair six-sided die. If you roll a 2 or 4, you win 5.00$$; otherwise, you win nothing. What is your expected value? Round to the nearest cent.

Accepted Answer

$$-0.67$$

Question 4

Suppose that 10% of people are left-handed. If 7 people are selected at random, what is the probability that exactly 2 of them are left-handed? Use the binomial formula.

Accepted Answer

$$0.124$$

Question 5

A test consists of 10 true/false questions. To pass, a student must answer at least 6 correctly. If a student guesses on each question, what is the probability that the student will pass? Round to three decimal places.

Accepted Answer

$$0.377$$

Question 6

Given $$n = 1205$$ and $$p = 0.98$$, find the minimum value that is not significantly low using the $$\mu - 2\sigma$$ rule. Round to the nearest hundredth.

Accepted Answer

$$1171.18$$

Question 7

The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. What is the probability that a pregnancy lasts 272 days or longer?

Accepted Answer

$$0.3936$$

Question 8

Red blood cell counts of women are normally distributed with a mean of $$4.577$$ million cells per microliter and a standard deviation of $$0.382$$ million. What percentage of women have red blood cell counts in the normal range from $$4.2 to$$ $$5.4$$ million cells per microliter? Round to the nearest percent.

Accepted Answer

$$83\%$$

Question 9

The incomes of trainees at a local mill are normally distributed with a mean of $$1100$$ and a standard deviation of $$150. $$What percentage of trainees earn less than $$900 a $$month?

Accepted Answer

$$12\%$$

Question 10

Human body temperatures are normally distributed with a mean of $$98.20^\circ F$$ and a standard deviation of $$0.62^\circ F. $$What temperature separates the top $$7\%$$ from the bottom $$93\%$$? Round to the nearest hundredth.

Accepted Answer

$$99.12^\circ F$$

Question 11

Replacement times for washing machines are normally distributed with a mean of $$10.4$$ years and a standard deviation of $$1.8$$ years. Find the replacement time that separates the top $$18\%$$ from the bottom $$82\%. $$Round to the nearest hundredth.

Accepted Answer

$$12.11$$ years

Question 12

The time it takes a mechanic to rebuild a transmission for a 2010 Chevrolet Colorado is normally distributed with a mean of $$8.4$$ hours and a standard deviation of $$1.8$$ hours. If $$40$$ mechanics are randomly selected, what is the probability that their mean rebuild time is less than $$8.9$$ hours?

Accepted Answer

$$0.9608$$

Question 13

The weights of fish in a certain lake are normally distributed with a mean of $$16 lb $$and a standard deviation of $$9 lb. If$$ $$19$$ fish are randomly selected, what is the probability that the mean weight will be between $$13.6$$ and $$19.6 lb$$?

Accepted Answer

$$0.6731$$

Question 14

A batch of 7 adults is selected at random. If the probability that an adult watches prime-time TV live is $$0.8$$, what is the probability that fewer than 3 of the selected adults watch prime-time live?

Accepted Answer

$$0.005$$

Question 15

If $$X is a $$binomial random variable with $$n = 10$$ and $$p = 0.2$$, what is the expected value $$E[X]$$?

Accepted Answer

$$2$$

Question 16

A normal distribution has mean $$\mu = 50$$ and standard deviation $$\sigma = 5. $$What is the $$z-$$score for $$x = 62$$?

Accepted Answer

$$2.4$$

Question 17

If $$P(A) = 0.3$$, $$P(B) = 0.5$$, and $$A$$ and $$B$$ are mutually exclusive, what is $$P(A \cup B)$$?

Accepted Answer

$$0.8$$

Question 18

If a continuous random variable $$X is $$normally distributed with mean $$\mu$$ and standard deviation $$\sigma$$, what is the probability that $$X is $$exactly equal to $$\mu$$?

Accepted Answer

$$0$$

Question 19

A fair coin is tossed 5 times. What is the probability of getting exactly 3 heads?

Accepted Answer

$$0.3125$$

Probability Distributions and Normal Distribution Applications in Statistics

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