Question

Hello, my name is Veronica Robles. I am in Math 1342 stastistics online at San Jacinto College. I am having trouble with this question.

In a survey of a group of men, the heights in the 20-29 age group were normally distributed, with a mean of 68.3 inches and a standard deviation of 3.0 inches. A study participant is randomly selected. Complete parts b, and c.

I am having trouble with part b and C in these questions.

B.(b) Find the probability that a study participant has a height that is between 68 and 70 inches.

The probability that the study participant selected at random is between 68 and 70 inches tall is ________ ( Round to four decimal places as needed.)

c. Find the probability that a study participant has a height that is more than 70 inches.

The probability that the study participant selected at random is more than 70 inches tall is ______ ( Round to four decimal places as needed)

Can you please explain to me about this two problems that of the z score. I can have better understanding . Thank you.

Step 1

Given heights in 20-29 age group were normally distributed with mean = 68.3 inches and standard deviation = 3.0 inches

A study participant is randimly selected and we need to determine the probability that participant height is betweem 68 and 70 inches.

Let X be the distribution which describes the heights in 20-29 age group.

here we need P( 68 < X < 70).

Step 2

We know X is normally distributed with men 68.3 and standard deviation 3. So we convert the X scores to Z scores,

Z score is the distance of a data point from mean of the distriution in terms of the standard deviation and it is given by the below mentioned formula.

after substituting X = 68, X = 70 we find Z scores for them -0.1 and 0.57 respectively.

converting into Z scores we get P( 68 < X < 70) = P( -0.1 < Z < 0.57)

Step 3

P(-0.1 < Z < 0.57) this is nothing bu tthe area between -0.1 and 0.57 in a standard normal curve. The total area to left of 0.57 is P(Z < 0.57) and the total area to the left of -0.1 i...

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