Question

Assume the data set described is normally distributed with the given mean and standard deviation, and with n

total values. Find the approximate number of data values that will fall in the given range.

Mean= −14.5

Standard deviation= 1.7

n= 120

Range: −17.9 to −11.1

in this case, we expect about data values to fall between -17.9 and −11.1

Answer 1

Given:

= -14.5, = 1.7

Find: P(-17.9 < X < -11.1)

P(-17.9 < X < -11.1) = P(-2 < Z < 2)

P(-17.9 < X < -11.1) = P(Z < 2) - P(Z < -2)

P(-17.9 < X < -11.1) = 0.9772 - 0.0228         .....Using standard Normal table

P(-17.9 < X < -11.1) = 0.9545