Question 1

Given the probability distribution for the number of defective computers in a batch of 4: $$P(0) = 0.4521$$, $$P(1) = 0.3970$$, $$P(2) = 0.1307$$, $$P(3) = 0.0191$$, $$P(4) = 0.0010$$, what is the standard deviation of the distribution? (Round to the nearest hundredth.)

Accepted Answer

$$\eta = 0.77$$

Question 2

A contractor faces a profit of $$20,000 with probability 0.7 or a loss of 17$$,000 with probability 0.3. What is the expected profit?

Accepted Answer

$$8,900$$

Question 3

In a survey of 300 college graduates, 53% reported entering a profession related to their major. If 9 are randomly selected without replacement, what is the probability that exactly 3 entered a related profession?

Accepted Answer

0.135

Question 4

For a binomial distribution with $$n = 4$$, $$x = 3$$, and $$p = \frac{1}{6}$$, what is $$P(x=3)$$? (Round to three decimal places.)

Accepted Answer

0.015

Question 5

Find the mean $$\mu$$ for a binomial distribution with $$n = 44$$ and $$p = 0.2. ($$Round to the nearest tenth.)

Accepted Answer

$$\mu = 8.8$$

Question 6

Find the standard deviation $$\eta$$ for a binomial distribution with $$n = 21$$ and $$p = 0.2. ($$Round to the nearest hundredth.)

Accepted Answer

$$\eta = 1.83$$

Question 7

Refer to the first image. What is the area of the shaded region under the standard normal curve?

Accepted Answer

0.8708

Question 8

Refer to the second image. If the shaded area is $$0.9599$$, what is the corresponding $$z$$ score?

Accepted Answer

1.75

Question 9

A thermometer is randomly selected from a batch with mean reading $$0^\circC $$and standard deviation $$1^\circC. $$What is the temperature reading at the 96th percentile ($$P_{96}$$)?

Accepted Answer

1.75$$^\circ$$

Question 10

If 7% of thermometers are rejected for being too low, what temperature separates the rejected thermometers from the others? (Assume normal distribution with mean $$0^\circC $$and standard deviation $$1^\circC.)$$

Accepted Answer

-1.48$$^\circ$$

Question 11

If $$z is a $$standard normal variable, what is the probability that $$z$$ lies between $$0$$ and $$3.01$$?

Accepted Answer

0.4987

Question 12

If $$z is a $$standard normal variable, what is the probability that $$z is $$greater than $$-1.82$$?

Accepted Answer

0.9656

Question 13

Assume $$X is $$normally distributed with mean $$\mu = 60.0$$ and standard deviation $$\eta = 4.0. $$What is $$P(X \u003c 53.0)$$?

Accepted Answer

0.0401

Question 14

Refer to the third image. What is the area of the shaded region under the standard normal curve?

Accepted Answer

0.2776

Question 15

A pharmaceutical company claims that 80% of patients experience relief from a new drug. If 10 patients are treated, what is the probability that exactly 8 experience relief? Use the binomial probability formula.

Accepted Answer

$$P(X=8) = 0.302$$

Question 16

A quality control manager tests 15 light bulbs and finds that the probability a bulb is defective is 0.1. What is the expected number of defective bulbs?

Accepted Answer

$$\mu = 1.5$$

Question 17

A hospital finds that the time to recovery from a certain surgery is normally distributed with mean 8 days and standard deviation 2 days. What is the probability a randomly selected patient recovers in less than 5 days?

Accepted Answer

0.0668

Question 18

A standardized test has scores that are normally distributed with mean 500 and standard deviation 100. What score corresponds to the 90th percentile?

Accepted Answer

628

Study Guide: Standard Normal Distribution and Probability Areas

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