The heights of female students in a university are approx normally distributed with a mean of...

The heights of female students in a university are approx normally distributed with a mean of 162 cm and a standard dev of 8 cm. Explain your answers.

a) Approx 68% of all female students in a university will have heights between ____ cm and ____ cm.

b) Heights greater than ____ cm would be considered peculiar.

Solutions

Expert Solution

Given that,

mean = = 162

standard deviation = = 8

middle 68% of score is

P(-z < Z < z) = 0.68

P(Z < z) - P(Z < -z) = 0.68

2 P(Z < z) - 1 = 0.68

2 P(Z < z) = 1 + 0.68 = 1.68

P(Z < z) = 1.68 / 2 = 0.84

P(Z < 0.99) = 0.84

z ±0.99

z = - 0.99

Using z-score formula

x= z * +

x= - 0.99 *8+162

x=154.08

z = 0.99

Using z-score formula

x= z * +

x= 0.99*6+162

x= 167.94

Approx 68% of all female students in a university will have heights between 154.08 cm and 167.94

orchestra answered 1 year ago

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