3 years ago

50 POINTS !!

1 answer:

4 0

Answer:

Step-by-step explanation:

Hope this helps u!!

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Nutka1998 [239]

Answer:

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

Step-by-step 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 = $\frac{X-\mu}{\sigma}$ ~ 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( $\frac{X-\mu}{\sigma}$ > $\frac{65-68}{3}$ ) = 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.

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3 years ago