Question

Attendance at large exhibition shows in Denver averages about 7970 people per day, with standard deviation of about 505. 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

Given,

= 7970 , = 505

We convert this to standard normal as

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

a)

P( X < 7200) = P( Z < 7200 - 7970 / 505)

= P( Z < -1.5248)

= 1 - P (Z < 1.5248)

= 1 - 0.9363

= 0.0637

b)

P( X > 8900) = P( Z > 8900 - 7970 / 505)

= P( Z > 1.8416)

= 1 - P( Z < 1.8416)

= 1 - 0.9672

= 0.0328

c)

P(7200 < X < 8900) = P( X < 8900) - P( X < 7200)

= P( Z < 8900 - 7970 / 505) - P( Z < 7200 - 7970 / 505)

= P( Z < 1.8416) - P( Z < -1.5248)

= P( Z < 1.8416) - ( 1 - P( Z < 1.5248) )

= 0.9672 - ( 1 - 0.963)

= 0.9035