Question

Attendance at large exhibition shows in Denver averages about 8000 people per day, with standard deviation of about 500. Assume that the daily attendance figures follow a normal distribution. (Round your answers to four 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

Probability function of normal distribution f(x) = 1/sigma squareroot 2 pi exp [-1/2 (x - mu/sigma)^2] where mu = mean = 8000 sigma = s.d = 500 f(x) = 1/500 squareroot 2 pi exp [-1/2 (x - 8000/500)^2] a) p(x lessthanorequalto 7200) = f(7200) = phi (7200 - 8000/500) = phi (-16) = 1 - phi(1.6) = 1 - 0.9452 = 0.0548 TildeEqual 5.48% Here f(x) is distribution function and phi (z) is standardized distribution function. F(x) = phi (x - mu/sigma) we can find out value of phi (z) from normal distribution table (see table 47 of advance engineering mathematics book by Erwin reyszig) P(x greaterthanorequalto 8900) = 1 - p(x lessthanorequalto 8900) = 1 - F(x = 8900) = 1 - phi (8900 - 8000/500) = 1 - phi (1.8) = 1 - 0.9461 = 0.0539 = 5.39% P(7200 lessthanorequalto x lessthanorequalto 8900) F(x = 8900) - F(x =