Question

A sample of final exam scores is normally distributed with a mean equal to 25 and a variance equal to 16.

Part (a)

What percentage of scares are between 21 and 29? (Round your answer to two decimal places)

Part (b)

What raw score is the cutiff for the top 10% of scores? (Round your answer to one decimal place)

Part (c)

What is the proportion below 20? (Round your answer to four decimal places)

Part (d)

What is the probability of a score less than 30? (Round your answer to four decimal places)

Answer 1

Solution :

(a)

P(21 < x < 29) = P[(21 - 25)/ 4) < (x - ) /  < (29 - 25) / 4) ]

= P(-1 < z < 1)

= P(z < 1) - P(z < 1)

= 0.8413 - 0.1587

= 0.6826

68.26%

(b)

P(Z > 1.28) = 0.10

z = 1.28

Using z-score formula,

x = z * +

x = 1.28 * 4 + 25 = 30.1

Cutoff score = 30.1

(c)

P(x < 20) = P[(x - ) / < (20 - 25) / 4]

= P(z < -1.25)

= 0.1056

(d)

P(x < 30) = P[(x - ) / < (30 - 25) / 4]

= P(z < 1.25)

= 0.8944