Answer to Question #187107 in Statistics and Probability for Limpo

Question #187107

The probability of women is distributed with the mean of 60kg and standard deviation 5kg. What is the probability that chosen at random

1. Greater than 70

2. Between 61&65

3. Less than 55


1
Expert's answer
2021-05-07T10:32:38-0400

Solution:

Given, "\\mu=60,\\sigma=5"

"X\\sim Bin(\\mu,\\sigma)"

1. "P(X>70)=P(z>\\dfrac{70-60}{5})=P(z>2)"

"=1-P(z\\le2)=1-0.97725=0.02275"

2. "P(61\\le X\\le 65)=P(\\dfrac{61-60}{5}\\le z\\le \\dfrac{65-60}{5})"

"=P(0.2\\le z\\le1)=P(z\\le1)-P(z\\le0.2)=0.84134-0.57926\n\\\\=0.26208"

3. "P(X<55)=P(z<\\dfrac{55-60}{5})=P(z<-1)=0.15866"


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