Question

Suppose a normal distribution has a mean of 26 and a standard deviation of 4. What is the probability that a data value is between 28 and 35? Round your answer to the nearest tenth of a percent.
A. 29.6%
B. 23.6%
C. 27.6%
D. 25.6%

Answer 1

Using the normal distribution, it is found that the probability that a data value is between 28 and 35 is given by:

A. 29.6%.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean $\mu$ and standard deviation $\sigma$ is given by:

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

• The z-score measures how many standard deviations the measure is above or below the mean.

• Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

Researching the problem on the internet, the mean and the standard deviation are given by:

$\mu = 26, \sigma = 4$.

As a proportion, the probability that a data value is between 28 and 35 is the p-value of Z when X = 35 subtracted by the p-value of Z when X = 28, hence:

X = 35:

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

$Z = \frac{35 - 26}{4}$

Z = 2.25

Z = 2.25 has a p-value of 0.988.

X = 28:

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

$Z = \frac{28 - 26}{4}$

Z = 0.5

Z = 0.5 has a p-value of 0.692.

0.988 - 0.692 = 0.296 = 29.6%, which means that option A is correct.

More can be learned about the normal distribution at https://brainly.com/question/24663213

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Answer 2

Answer:

A

Step-by-step explanation:

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