Question

Distributions:

1. List the characteristics of a normal distribution.
2. The weights of baby boys at six months is normally distributed with a mean of 17.25 lbs. and a standard deviation of 2.0 lbs. By an age of twelve months, the mean increases to 22.50 lbs. and the standard deviation is 2.2 lbs.
   1. Which age group has the wider distribution?
   2. What percentage of the twelve-month old boys weigh more than 26.9 lbs.?
   3. What percentage of six-month old boys weigh between 15.25 lbs. and 19.25 lbs.?
   4. A twelve-month old boy who weighs 24.7 lbs. is what percentile for weight?
3. In the mailroom, the mean weight of a letter 25.0 grams. The standard deviation is 0.1 grams. A first-class stamp is sufficient postage to mail a letter with a maximum weight of 28 grams. On a given day, the post office in downtown processes an average of 12,370 pieces of mail with a first-class stamp as postage. If the letter weight is normally distributed, approximately how many of these letters will need additional postage?

Answer 1

Result:

(first 2 questions answered)

List the characteristics of a normal distribution.

Symmetric, bell shaped

Continuous for all values of X between -∞ and ∞

Described by Two parameters, μ and σ.

Approximately 68% of values in the distribution are within 1 SD of the mean,

Approximately 95% of values in the distribution are within 2 SD of the mean.

Approximately 99% of values in the distribution are within 3 SD of the mean.

Mean = median = mode

The weights of baby boys at six months is normally distributed with a mean of 17.25 lbs. and a standard deviation of 2.0 lbs. By an age of twelve months, the mean increases to 22.50 lbs. and the standard deviation is 2.2 lbs.

Which age group has the wider distribution?

age of twelve months is wider since its standard deviation is large.

What percentage of the twelve-month old boys weigh more than 26.9 lbs.?

Z value for 26.9, z =(26.9-22.50)/2.2 =2.0

P( x > 26.9) = P( z >2.0)

=0.0228

The required percentage= 2.28%

Excel function used:=1-NORM.S.DIST(2,TRUE)

What percentage of six-month old boys weigh between 15.25 lbs. and 19.25 lbs.?

Z value for 15.25, z =(15.25-17.25)/2.0 = -1

Z value for 19.25, z =(19.25-17.25)/2.0 = 1

P( 15.72<x<19.25) = P(-1<z<1)=P( z <1)-P( z< -1)

     = 0.8413- 0.1587 =0.6826

The required percentage= 68.26%

A twelve-month old boy who weighs 24.7 lbs. is what percentile for weight?

Z value for 24.7, z =(24.7-22.50)/2.2 =1

P( z <1)=0.8413

The required percentile = 84.13