Question

Suppose X is normally distributed. Which of the following is the probability question equivalent to “What is the area under the curve to the right of 16.5?”

A. What is P(X>24.2)?
B. What is P(X<24.2)?
C. What is P(16.5<X<24.2)?
D. What is P(X<16.5)?
E. What is P(X>16.5)?

True or false: As the sample size increases, the mean of the distribution of sample means increases.

True or false: As the sample size increases, the standard error increases.

True or false: If the sample size is at least 30, you can apply the CLT to conclude that the distribution of x¯ is approximately normal and hence that you can compute the probability that x¯ is within a given interval using normalcdf.

In 2016, the mean annual salary for registered nurses in Virginia was approximately $62,350. A sample of 30 Virginia registered nurses was taken. What is the probability that the sample mean was less than $61,446? Assume that σ= 7,500.

A. 0.2546
B. 0.7454
C. Can’t work this; normality of x¯ not satisfied
D. 0.4520

The average height of an adult American woman is 64 inches. Assume that σ= 3.1 inches. A sample of 39 adult American women was taken. What is the probability that the x¯ was less than 65 inches for this sample?

A. Can’t work this; normality of x¯ not satisfied
B. 0.6265
C. 0.9780
D. 0.0220

Answer 1

From the given information,

The required correct answers are,

1. What is P(X>16.5)?

i.e. Option E. is correct.

2. It is false statement because there is no effect of increasing or decreasing the sample size on mean of the distribution of sample means.

3. It is false statement because as sample size increases, standard error decreases.

4. It is true statement.

5. P(Xbar<61446)= 0.2546

i.e., Option A. is correct.

6. P(Xbar<65)= 0.9780

i.e., Option C. is correct.

Thank you.

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