Question

Suppose a normal distribution has a mean of 98 and a standard deviation of 6. What is P(x<110)? (The greater than sign is actually greater than or equal to)

A. 0.975
B. 0.025
C. 0.16
D. 0.84

Answer 1

Using the normal distribution, the probability that x is less than 110 is:

A. 0.975.

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.

The mean and the standard deviation are given as follows:

$\mu = 98, \sigma = 6$

The probability is the p-value of Z when X = 110, hence:

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

$Z = \frac{110 - 98}{6}$

Z = 2

Z = 2 has a p-value of 0.975.

Hence option A is correct.

More can be learned about the normal distribution at https://brainly.com/question/15181104

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