Question

A health researcher has data on the body mass of 1000 male patients.
The mean value is 80kg and the standard deviation is 15kg. Assuming
the values are normally distributed, about how many patients have
body mass between 65 and 95kg (65kg < mass < 95kg)?

Answer 1

mean = 80

standard deviation = 15

P( 65 < x< 95)

P( -1 < z <1)

The probability that -1 < Z < 1 is equal to the blue area under the curve.

P (−1<Z<1 )=P ( Z<1 )−P (Z<−1 )

From Standard Normal Table P ( Z<1 )=0.8413.

P ( Z < −1)= 1 − P ( Z < 1 )=1−0.8413=0.1587

Hence P (−1 < Z < 1 )=0.6826

No of patients = 1000 * 0.6826 = 682.6 i.e. 682