Question 1

Given a normal distribution with mean $$\mu = 90$$ and standard deviation $$\sigma = 6$$, find the value of $$a$$ such that $$P(x \u003e a) = 0.95. $$Which of the following is correct?

Accepted Answer

$$a = 80.13$$

Question 2

If $$X \sim N(500, 100^2$)$$, what is the value of $$x$$ such that $$P(x \u003c a) = 0.6$$?

Accepted Answer

$$a = 525$$

Question 3

For a normal distribution, which formula is used to find the value $$a$$ corresponding to a given $$z-$$score?

Accepted Answer

$$a = \mu + \sigma z$$

Question 4

The ages of subjects with Alzheimer’s disease are normally distributed with mean $$80$$ and standard deviation $$16. $$Find $$a$$ such that $$P(x \u003e a) = 0.9.$$

Accepted Answer

$$a = 59.52$$

Question 5

Given $$P(x \u003c a) = 0.975$$ for a normal distribution with mean $$80$$ and standard deviation $$16$$, what is the value of $$a$$?

Accepted Answer

$$a = 111.36$$

Question 6

The lifespan of palm trees is normally distributed with mean $$70$$ years and standard deviation $$1.5$$ years. Find $$a$$ such that $$P(x \u003c a) = 0.21.$$

Accepted Answer

Question 7

Which of the following statements is TRUE about the sign of the $$z-$$score when finding $$a$$ for $$P(x \u003e a)$$?

Accepted Answer

The sign of the $$z-$$score depends on whether $$a is $$above or below the mean.

Question 8

If $$P(x \u003c a) = 0.21$$ for $$X \sim N(70, 1.5^2$)$$, what is the corresponding $$z-$$score?

Accepted Answer

$$z = -0.81$$

Question 9

A hospital wants to know the age below which 97.5% of Alzheimer’s patients fall. If the ages are normally distributed with mean $$80$$ and standard deviation $$16$$, what is the answer?

Accepted Answer

$$111.36$$

Question 10

Which step is NOT necessary when using the inverse normal method to find $$a$$ for a given probability?

Accepted Answer

Multiply the mean by the standard deviation.

Question 11

If $$P(x \u003e a) = 0.05$$ for a normal distribution with mean $$100$$ and standard deviation $$10$$, what is the value of $$a$$?

Accepted Answer

$$a = 116.45$$

Question 12

A company finds that the weights of its products are normally distributed with mean $$50 kg $$and standard deviation $$4 kg. $$What is the weight $$a$$ such that $$P(x \u003c a) = 0.8413$$?

Accepted Answer

$$a = 54.6$$

Question 13

Which of the following best describes the use of the $$z-$$table in inverse normal problems?

Accepted Answer

To find the $$z-$$score for a given probability.

Question 14

If $$P(x \u003c a) = 0.5$$ for a normal distribution, what is the value of $$a$$?

Accepted Answer

$$a = \mu$$

Question 15

A test score is normally distributed with mean $$60$$ and standard deviation $$8. $$What score corresponds to the 90th percentile?

Accepted Answer

$$a = 70.24$$

Inverse Normal Calculations in the Normal Distribution

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