Question

The weights of kittens have a symmetric shape with mean of 3.6 pounds and a standard deviation of 0.4 pounds, answer each of the following:

a. What percent of kittens weigh between 2.8 and 4.8 pounds?

b. Which weight represents ?84.

Answer 1

Given:

= 3.6 pounds, = 0.4 pounds

Let X be the weight of kittens

a) P(2.8 < X < 4.8)

P(2.8 < X < 4.8) = P(-2 < Z < 3)

P(2.8 < X < 4.8) = P(Z < 3) - P(Z < -2)

P(2.8 < X < 4.8) = 0.9987 - 0.0228

P(2.8 < X < 4.8) = 0.9759 .......................Using standard Normal table

P(2.8 < X < 4.8) = 0.9759 = 97.59%

b)

Find: 84th percentile

P(X < Xo) = 84% = 0.84

P(X < 0.9945) = 0.84 ....................................From Normal distribution table,

Or by using Invnorm function, Invnorm(0.84) = 0.9945

Therefore, The required value of X is,

Z = (X - ) /

0.9945 = (X - 3.6) / 0.4

X - 3.6 = 0.40

X = 3.6 + 0.40

X = 4

4 pounds represent 84th Percentile.