A distribution of measurements is relatively mound-shaped with mean 60 and stand

Question

A distribution of measurements is relatively mound-shaped with mean 60 and standard deviation 10.

(a) What approximate proportion of the measurements will fall between 50 and 70? (Enter your answer to two decimal places.)

(b) What approximate proportion of the measurements will fall between 40 and 80? (Enter your answer to two decimal places.)

(c) What approximate proportion of the measurements will fall between 40 and 70? (Enter your answer to three decimal places.)

(d) What approximate proportion of the measurements will be greater than 70? (Enter your answer to two decimal places.)

Explanation / Answer

Here we will convert x to standard normal variables and find required probability

a. P(50<x<70)=P(50-60/10<z<70-60/10)=P(-1<z<1)=0.6827

b. P(40<x<80)=P(-2<z<2)=0.9545

c. P(40<x<70)=P(-2<z<1)=0.8186

d. P(x>70)=P(z>1)=0.1587

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