Question

let x be a random variable that represents the length of time it takes a student to complete a MTH 23 exam.It was found that x has an approximately normal distribution with mean =1.5 hours and standard deviation =.25 hours.

(a) What is the probability that it takes at least 1.4 hours for a randomly selected student to complete the exam?

(b) Suppose 25 student are selected at random. What is the probability that the means time of completing the exam for these 25 students is no more than 1.4 hours?

Answer 1

a)

mean = 1.5,s = 0.25

P(x>1.4)

=P(z > (1.4 - 1.5)/(0.25/sqrt(23))
= P(z> -1.92)
= 0.9725

2)

P(x< 1.4) when n =25

=P(z < (1.4 - 1.5)/(0.25/sqrt(25))
= P(z < -2)
= 0.0228