Question

Height of 10th grade boys is normally distributed with a mean of 63. 5 in, and a standard deviation

of 2. 9 in.

The area greater than the z-score is the probability that a randomly selected 14-year old boy

exceeds 70 in.

What is the probability that a randomly selected 10th grade boy exceeds 70 in. ?

Use your standard normal table.

Answer 1

Using the normal distribution, it is found that there is a 0.0125 = 1.25% probability that a randomly selected 10th grade boy exceeds 70 in.

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.

In this problem, the mean and the standard deviation are, respectively, given by $\mu = 63.5, \sigma = 2.9$.

The probability that a randomly selected 10th grade boy exceeds 70 in is one subtracted by the p-value of Z when X = 70, hence:

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

$Z = \frac{70 - 63.5}{2.9}$

Z = 2.24

Z = 2.24 has a p-value of 0.9875.

1 - 0.9875 = 0.0125.

0.0125 = 1.25% probability that a randomly selected 10th grade boy exceeds 70 in.

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

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