Question

Suppose a fair director in a certain city imposes a height limit on an amusement park ride called Death drop, due to safety concerns. Patrons must be at least 4 feet tall to ride Death Drop. Suppose patrons’ heights in this city follow a Normal distribution with a mean of 5 feet and a standard deviation of 0.9 feet.

a) What is the probability that a randomly selected patron would be tall enough to ride Death Drop?

b) A separate amusement park ride is dedicated to patrons who are shorter than 3.5 feet. What is the probability that a randomly selected patron would be shorter than 3.5 feet?

Answer 1

Solution :

Given that ,

mean = = 5

standard deviation = = 0.9

a) P(x > 4) = 1 - p( x< 4)

=1- p P[(x - ) / < (4 - 5 ) /0.9 ]

=1- P(z < -1.11)

Using z table,

= 1 - 0.1335

= 0.8665

b) P(x < 3.5) = P[(x - ) / < (3.5 - 5) / 0.9 ]

= P(z < -1.67)

Using z table,

= 0.0475