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The heights of 18-year-old men are approximately normally distributed with mean 68 inches and standard deviation 3 inches. What is the probability that an 18-year-old man selected at random is greater than 65 inches tall? Round your answer to four decimal places.

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Answer:

The probability that an 18-year-old man selected at random is greater than 65 inches tall is 0.8413.

Explanation:

We are given that the heights of 18-year-old men are approximately normally distributed with mean 68 inches and a standard deviation of 3 inches.

Let X = heights of 18-year-old men.

So, X ~ Normal(
\mu=68,\sigma^(2) =3^(2))

The z-score probability distribution for the normal distribution is given by;

Z =
(X-\mu)/(\sigma) ~ N(0,1)

where,
\mu = mean height = 68 inches


\sigma = standard deviation = 3 inches

Now, the probability that an 18-year-old man selected at random is greater than 65 inches tall is given by = P(X > 65 inches)

P(X > 65 inches) = P(
(X-\mu)/(\sigma) >
(65-68)/(3) ) = P(Z > -1) = P(Z < 1)

= 0.8413

The above probability is calculated by looking at the value of x = 1 in the z table which has an area of 0.8413.

User Azadeh
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