Question

The average speed of passenger trains travelling from Kyoto to Tokyo have been found to be normally distributed with a mean of 250 km per hour and a standard deviation of 30 km per hour.

a. What is the probability that a train will average less than 200 km per hour?

b. What is the probability that a train will average more than 300 km per hour?

c. What is the probability that a train will average between 210 and 280 km per hour?

do all and do not handwritten please type it

Answer 1

Solution :

a ) Given that ,

mean = = 250

standard deviation = =30

P(x < 200) = P[(x - ) / < (200-250)/30 ]

= P(z < -1.67)

= 0.0475

probability = 0.0475

b) P(x > 300) = 1 - P(x < 300)

= 1 - P[(x - ) / < (300-250) /30 )

= 1 - P(z < 1.67)   

= 1 - 0.9525  = 0.0475

Probability = 0.0475 c) P(210 < x <280 ) = P[(210-250)/ 30) < (x - ) /  < (280-250) /30 ) ]

= P(-1.33 < z <1 )

= P(z < 1) - P(z < -1.33)

= 0.8413 - 0.0918 = 0.7495

Probability = 0.7495