Question

Consider a normal distribution, with a mean of 75 and a standard deviation of 10. What is the probability of obtaining a value:

a. between 75 and 10?

b. between 65 and 85?

c. less than 65?

d. greater than 85?

Answer 1

P(X < A) = P(Z < (A - mean)/standard deviation)

Mean = 75

Standard deviation = 10

a. P(between 75 and 10) = P(10 < X < 75)

= P(X < 75) - P(X < 10)

= 0.5 - P(Z < -6.5)

= 0.5 - 0

= 0.5

b. P(between 65 and 85) = P(65 < X < 85)

= P(X < 85) - P(X < 65)

= P(Z < (85 - 75)/10) - P(Z < (65 - 75)/10)

= P(Z < 1) - P(Z < -1)

= 0.8413 - 0.1587

= 0.6826

c. P(less than 65) = P(X < 65)

= P(Z < -1)

= 0.1587

d. P(greater than 85) = P(X > 85)

= 1 - P(X < 85)

= 1 - P(Z < 1)

= 1 - 0.8413

= 0.1587