According to a study done by De Anza students, the height for Asian adult males is normally distributed with an average of 66 inches and a standard deviation of 2.5 inches. Suppose one Asian adult male is randomly chosen. Let X = height of the individual. A) Give the distribution of X.

X ~ _ (,)

B) Find the probability that the person is between 64 and 69 inches.

Write the probability statement.

P(__

What is the probability?

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Respuesta :

JeanaShupp JeanaShupp · Answer 1 · 2019-07-19T08:22:18+02:00

Answer: A) [tex]X\sim N(66,2.5)[/tex]

B)0.6731

Step-by-step explanation:

Given : The height for Asian adult males is normally distributed with

Mean : [tex]\mu=66\text{ inches}[/tex]

Standard deviation : [tex]\sigma= 2.5\text{ inches}[/tex]

Let X = height of the individual.

A) The distribution of X is given by :-

[tex]X\sim N(\mu,\sigma)\\\\\Rightarrow\ X\sim N(66,2.5)[/tex]

B) The formula to find the z-score is given by :-

[tex]z=\dfrac{x-\mu}{\sigma}[/tex]

For , x= 64

[tex]z=\dfrac{64-66}{2.5}=-0.8[/tex]

For , x= 69

[tex]z=\dfrac{69-66}{2.5}=1.2[/tex]

Now, the required probability :-

[tex]P(64<x<69)=P(-0.8<z<1.2)=P(z<1.2)-P(z<0.8)\\\\=0.8849303-0.2118554=0.6730749\approx0.6731[/tex]

Hence, the probability that the person is between 64 and 69 inches is 0.6731.