Question 1

A random variable $$X is $$uniformly distributed between 2 and 6. What is the probability that $$X \u003e 4$$?

Accepted Answer

$$0.5$$

Question 2

Given a standard normal distribution, what is the area under the curve to the left of $$z = 1.13$$?

Accepted Answer

$$0.8708$$

Question 3

If the shaded area under the standard normal curve is $$0.0694$$, what is the corresponding $$z-$$score?

Accepted Answer

$$z = 1.48$$

Question 4

For a standard normal variable $$z$$, what is $$P(-2.41 \u003c z \u003c 0)$$?

Accepted Answer

$$0.4920$$

Question 5

What is the probability that $$z$$ lies between $$-0.73$$ and $$2.27 in a $$standard normal distribution?

Accepted Answer

$$0.7557$$

Question 6

A thermometer is tested at the freezing point of water. The readings are normally distributed with mean $$0^	ext{o}C$$ and standard deviation $$1^	ext{o}C. $$What is the 40th percentile ($$P_{40}) of $$the readings?

Accepted Answer

$$-0.25^	ext{o}C$$

Question 7

For a standard normal distribution, what percentage of data is more than 1 standard deviation away from the mean?

Accepted Answer

$$31.74\%$$

Question 8

Refer to the first image (IQ scores, mean $$=100$$, SD $$=15). $$What is the area of the shaded region to the left of $$110$$?

Accepted Answer

$$0.7486$$

Question 9

Refer to the second image (IQ scores, mean $$=100$$, SD $$=15). If $$the shaded area under the curve is $$0.5675$$, what is the corresponding IQ score?

Accepted Answer

$$102.6$$

Question 10

Scores on a test are normally distributed with mean $$67.7$$ and standard deviation $$9.3. $$What is the 81st percentile ($$P_{81}$$)?

Accepted Answer

$$75.9$$

Question 11

If $$X is $$normally distributed with mean $$\mu = 60.0$$ and standard deviation $$\sigma = 4.0$$, what is the probability that $$X \u003c 53.0$$?

Accepted Answer

$$0.0401$$

Question 12

The diameters of bolts produced by a machine are normally distributed with mean $$0.30$$ inches and standard deviation $$0.01$$ inches. What percentage of bolts will have a diameter greater than $$0.32$$ inches?

Accepted Answer

$$2.28\%$$

Question 13

When using the normal distribution as an approximation to the binomial, which region corresponds to the probability of more than 35 correct answers?

Accepted Answer

The area to the right of 35.5

Question 14

A binomial experiment has $$n = 20$$ and $$p = 0.60. $$Estimate $$P($$fewer than $$8)$$ using the normal approximation.

Accepted Answer

$$0.0202$$

Question 15

In a hospital, 90 babies are born. What is the probability of getting exactly 43 boys, assuming the probability of a boy is $$0.5$$? Use the normal approximation.

Accepted Answer

$$0.0764$$

Question 16

A researcher wants to find the $$z-$$score that separates the bottom 10% from the top 90% in a standard normal distribution. Which formula should be used?

Accepted Answer

Find $$z$$ such that $$P(Z \u003c z) = 0.10$$

Question 17

A quality control engineer wants to know the probability that a randomly selected bolt is between $$0.29$$ and $$0.31$$ inches in diameter, given $$\mu = 0.30$$ and $$\sigma = 0.01. $$Which steps are correct?

Accepted Answer

Convert $$0.29$$ and $$0.31 to$$ $$z-$$scores, then find the area between them.

Question 18

A standardized test has scores that are normally distributed with mean $$500$$ and standard deviation $$100. $$What is the probability that a randomly selected student scores above $$650$$?

Accepted Answer

$$0.0668$$

Question 19

If a normal distribution has mean $$\mu$$ and standard deviation $$\sigma$$, which formula gives the $$z-$$score for a value $$X$$?

Accepted Answer

$$z = \frac{X - \mu}{\sigma}$$

Question 20

A company claims that 95% of its products last more than 2 years. If product lifetimes are normally distributed with mean $$3$$ years and standard deviation $$0.5$$ years, what is the minimum lifetime for the top 5%?

Accepted Answer

$$3.82$$ years

Normal Distribution and Probability Guidance for Chapter 6

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