Question

Question 25 of 25Suppose the heights of the members of a population follow a normaldistribution. If the mean height of the population is 72 inches and thestandard deviation is 3 inches, 99.7% of the population will have a heightwithin which range?OA. 63 inches to 81 inchesOB. 66 inches to 78 inchesOC. 69 inches to 75 inchesOD 60 inches to 84 inches

Answer 1

Hello there. To solve this question, we'll have to remember some properties about normal distribution and finding values in the normal table.

Given that the heights of the members of a population, that follows a normal distribution, has mean height of 72 inches and standard deviation of 3 inches, we say that for this population height X, the continuous random variable,

`X\text{\textasciitilde}N(\mu=72,\sigma=3)`

We would first like to use a padronized continuous random variable. For this, we use the following transformation:

`Z=(X-\mu)/(\sigma)`

First, notice that we want to determine the values of x in a range [x1, x2] such that

`P(x_1\leq X\leq x_2)=0.997`

That is the probability of finding someone with a height between these values