Question

The heights of 2000 students are normally distributed with a mean of 165.5 centimeters and a standard deviation of 7.1 centimeters. Assuming that the heights are recorded to the nearest half-centimeter, how many of these students would be expected to have heights:

(a) less than 151.0 centimeters?

(b) Between 163.5 and 173.0 centimeters inclusive?

(c) Equal to 168.0 centimeters?

(d) Greater than or equal to 182.0 centimeters?

Answer 1

Let X denotes the height of a randomly selected student.

Here,

X ~ Normal(165.5, 7.1²)

a)

Number of students would be expected to have heights less than 151.0 centimeters = 2000*0.0206 = 41.2 41

b)

Number of students would be expected to have heights between 163.5 and 173.0 centimeters inclusive = 2000*0.4655 = 931

c) P( X = 168) = 0, since X is a continuous variable.

Number of students would be expected to have heights equal to 168.0 centimeters = 2000*0 = 0

d)

Number of students would be expected to have heights greater than or equal to 182.0 centimeters

= 2000*0.0101 = 20.2 20