angelbruhhh1213
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Heights of men in the United States are approximately normally distributed
with a mean of 70 inches and a standard deviation of 2.5 inches.
Part A: What is the probability that a randomly selected man will be taller than 75 inches?

Part B: According to our information, is 75 unusually tall for a man?

Respuesta :

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Answer:

a. P(X>75)=0.02275

b. Yes

Step-by-step explanation:

Given that the mean is 70 inches and the standard deviation is 2.5 inches.

-the probability that a random selection has a height greater than 75 inches is calculated as:

[tex]P(X>75)\\\# compute\ z-score\\z=\frac{\bar x-\mu}{\sigma}\\\\z=\frac{75-70}{2.5}\\\\=2.00\\\\\therefore P(X>75)=1-P(X<75)\\\\=1-0.97725\\\\=0.02275[/tex]

Hence, the probability of a random being taller than 75 inches is 0.02275

b. Based on the above information, 75 inches is unusually tall since it has a deviation of 2.5 inches more than the standard deviation.

Answer:

Part A: 2.5%

B: Yes, it is unusual because a height of 75 has a probability less than 5%

Step-by-step explanation:

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