Question

Attendance at large exhibition shows in Denver averages about 7830 people per day, with standard deviation of about 515. Assume that the daily attendance figures follow a normal distribution. (Round your answers to 4 decimal places.)

(a) What is the probability that the daily attendance will be fewer than 7200 people?


(b) What is the probability that the daily attendance will be more than 8900 people?


(c) What is the probability that the daily attendance will be between 7200 and 8900 people?

Answer 1

Solution :

Given that ,

mean = = 7830

standard deviation = = 515

a)

P(x < 7200) = P((x - ) / < (7200 - 7830) / 515)

= P(z < -1.22)

= 0.1112

Probability = 0.1112

b)

P( > 8900) = 1 - P( < 8900)

= 1 - P(( - ) / < (8900 - 7830) / 515)

= 1 - P(z < 2.08)

= 1 - 0.9812

= 0.0188

Probability = 0.0188

c)

P(7200 < < 8900) = P((7200 - 7830) 515/ <( - ) / < (8900 - 7830) / 515))

= P(-1.22 < Z <2.08)

= P(Z < 2.08) - P(Z < -1.22)

= 0.9812 - 0.1112

= 0.8700

Probability = 0.8700