Question

The Scholastic Aptitude Test (SAT) scores in mathematics at a certain high school are normally distributed, with a mean of 550 and a standard deviation of 100. What is the probability that an individual chosen at random has the following scores? (Round your answers to four decimal places.)

(a) greater than 650


(b) less than 450


(c) between 600 and 750

Use the table of areas under the standard normal curve to find the probability that a z-score from the standard normal distribution will lie within the interval. (Round your answer to four decimal places.)

z > −1.8

Answer 1

Solution :

Given that ,

(a)

P(x > 650) = 1 - P(x < 650)

= 1 - P[(x - ) / < (650 - 550) / 100)

= 1 - P(z < 1)

= 1 - 0.8413

= 0.1587

Probability = 0.1587

(b)

P(x < 450) = P[(x - ) / < (450 - 550) / 100]

= P(z < -1)

= 0.1587

Probability = 0.1587

(c)

P(600 < x < 750) = P[(600 - 550)/ 100) < (x - ) /  < (750 - 550) / 100) ]

= P(0.5 < z < 2)

= P(z < 2) - P(z < 0.5)

= 0.9772 - 0.6915

= 0.2857

Probability = 0.2857

Using standard normal table ,

P(z > -1.8) = 1 - P(z < -1.8) = 1 - 0.0359 = 0.9641