Question

Suppose the average speeds of passenger trains traveling from Newark, New Jersey, to Philadelphia, Pennsylvania, are normally distributed, with a mean average speed of 89 miles per hour and a standard deviation of 6.4 miles per hour. (a) What is the probability that a train will average less than 70 miles per hour? (b) What is the probability that a train will average more than 79 miles per hour? (c) What is the probability that a train will average between 91 and 98 miles per hour?

Answer 1

Given,

= 89, = 6.4

We convert this to standard normal as

P(X < x) = P( Z < x - / )

a)

P( X < 70) = P( Z < 70 - 89 / 6.4 )

= P( Z < -2.97)

= 1 - P( Z < 2.97)

= 0.0015

b)

P( X > 79) = P (Z > 79 - 89 / 6.4)

= P( Z > -1.5625)

= P( Z < 1.5625)

= 0.9409

c)

P( 91 < X < 98) = P( X < 98) - P( X < 91)

= P( Z < 98 - 89 / 6.4) - P( Z < 91 - 89 / 6.4)

= P( Z < 1.4063) - P( Z < 0.3125)

= 0.9202 - 0.6227

= 0.2975