Question

Suppose 150 people take a random knowledge test, and say the mean score was 100 out of 200 points, with a standard deviation of 40. Supposing the scores are distributed in a normal probability distribution. Approximately how many people got above a 180? What is the probability that someone got between a 91 and a 157 on the quiz? (Round your answer to three digits after the decimal).

Answer 1

Solution :

Given that ,

a) P(x > 180) = 1 - p( x< 180)

=1- p P[(x - $\mu$) / $\sigma$ < (180 - 100) / 40]

=1- P(z < 2.0 )

= 1 - 0.9772

= 0.0228

= 150 * 0.0228 = 3.42

= 3 people.

b) P( 91 < x < 157) = P[(91 - 100)/ 40) < (x - $\mu$) /$\sigma$  < (157 - 100) / 40) ]

= P(-0.225 < z < 1.425)

= P(z < 1.425) - P(z < -0.225)

Using z table,

= 0.923 - 0.411

= 0.512