Question

Use the table for Area Under the Standard Normal Curve to answer the question. Note: Round z-scores to the nearest hundredth and then find the required A values using the table.

The cholesterol levels of a group of young women at a university are normally distributed, with a mean of 189 and a standard deviation of 36. What percent of the young women have the following cholesterol levels? (Round your answers to one decimal place.)

(a) greater than 225
_________%

(b) between 194 and 220
_________%

Answer 1

A) Given data

Cholesterol levels of a group is normally distributed with

Mean Value (X')=189

Standard deviation (S)=36

We need to determine the percentage of Young women have the following cholesterol levels for the do two cases

a) Greater than 225

I.e P(X>225)

First determine the z score value

Z score=(X-X')/S

=(225-189)/36

=36/36=1

P(X>225)=P(Z>1)

=0.1587( From normal area tables)

So, required percentage=15.87=15.9%

b) between 194 and 220

I.e P(294<X<220)

For X=194

Z score=(X-X')/S

=(194-189)/36 =0.1388=0.14

For X=220

Z score=(X-X')/S

=(220-189)/36=0.86

P(194<X<220)=P(0.14<Z<0.86)

=0.2494 (From normal area tables)

So, required percentage=24.94=25%