Question

Show work please.

1) If the scores for a test have a mean of 70 and a standard deviation of 12, find the percentage of scores that will fall above 50.

A) 95.25% B) 95.54% C) 45.07% D) 45.54%

2)

The average age of a vehicle registered in the U.S. is 8 years. If a random vehicle is selected, find the probability that the age is between 80 and 110 months. Assume the standard deviation is 15.

A) .6667 B) .6815 C) .7066 D) .6347

Answer 1

Answer:

1.

Given,

Mean = 70

Standard deviation = 12

P(X > 50) = P((x-mu)/s > (50 - 70)/12)

= P(z > -1.67)

= 0.9525403 [since from z table]

= 0.9525

= 95.25%

Option A is right answer.

2.

To give the probability that the age is between 80 and 110 months

Mean = 8*12

= 96

P(80 < X < 110) = P((80 - 96)/15 < (x-mu)/s < (110 - 96)/15)

= P(-1.07 < z < 0.93)

= P(z < 0.93) - P(z < -1.07)

= 0.8238144 - 0.1423097 [since from z table]

= 0.6815

Option B is right answer.