Question

1. Use the following information for the next four problems. Suppose that the cholesterol levels of adult American women can be described by a normal model with a mean of 188 mg/dL and a standard deviation of 24 mg/dL.

   Which one of the following intervals will contain the central 95% of cholesterol levels?

   	a.	116 to 260
   	b.	164 to 212
   	c.	140 to 236
   	d.	186 to 190

5 points   

QUESTION 4

1. What percent of adult American women will have cholesterol levels above 230 mg/dL?

   a.

   22.66%

   b.

   1.75%

   c.

   95.99%

   d.

   4.01%

   Find the 33^rd percentile of the cholesterol levels. That is, below what value are the lowest 33% of women’s cholesterol levels?

   	a.	203.10
   	b.	195.92
   	c.	177.44
   	d.	122.72

   QUESTION 6

   Suppose that the cholesterol level for one particular adult American woman corresponds to a Z-score of 2.0. Which one of the following gives a correct interpretation of this Z-score?

   	a.	Her cholesterol level is 2% above average.
   	b.	Her cholesterol level is 2 mg/dL above average.
   	c.	Her cholesterol level is 2 mg/dL.
   	d.	Her cholesterol level is 2 standard deviations above average.

Answer 1

Let X be the cholestrol levels of adult American women

X~ N( 188, 242)

a) According to empirical rule, 95% of the data is comtained within 2 stanadard deviation of the mean

So, 95% confidence interval = ( 188 2*24)

= ( 188- 48, 188+48)

= (140, 236)

Answer-  

c.	140 to 236

b) Percent of adult american women will have cholestrol levels above 230

= P( X > 230)

= P( > )

= P( z > 1.75)

= 1- P( z <1.75)

= 1- 0.9599

=0.0401

= 4.01%
Answer- d) 4.01%

c) 33rd percentile

P( Z <z)= 0.33

P( Z < -0.44) =0.33

z = -0.44

   = -0.44

   = -0.44

X = 188 - 24*0.44

X= 177.44

value below which are the lowest 33% of women’s cholesterol levels is c.177.44

d) interpretation of this Z-score-

d. Her cholesterol level is 2 standard deviations above average.