Question

The average snowfall in the city of Morris is 40 cm per year with a standard deviation of 5 cm. Using a Normal model, what values should border the middle 68% of the model?

Select one:

a. 35.45 and 44.45

b. 34.00 and 45.00

c. 35.03 and 44.98          

d. 34.45 and 45.45

e. 35.75 and 44.75

Answer 1

Solution:-

Given that,

mean = = 40

standard deviation = = 5

Using standard normal table,

P( -z < Z < z) = 68%

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

= 2P(Z < z) - 1 = 0.68

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

= P(Z < z) = 1.68 / 2

= P(Z < z) = 0.84

= P(Z < 0.995) = 0.84

= z  ± 0.995

Using z-score formula,

x = z * +

x = -0.995 * 5 + 40

x = 35.03

Using z-score formula,

x = z * +

x = 0.995 * 5 + 40

x = 44.98

The middle 68% are from 35.03 and 44.98.

correct option is = c