normal distribution

Question

Attendance at large exhibition shows in Denver averages about 7900 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

This is an exercise in using z scores. The z-score tells you how many standard deviations your data point (x) is from the mean. Positive z scores are greater than the mean, negative are less than the mean.

z = (x-μ)/σ

1. x =your data point (7200 or 8900)
2. μ = the mean or average of the normal distribution = 7900
3. σ = the standard deviation = 500

(a) Compute the z-score for x = 7200. Find a z-score table in your book or on-line. Look up the value of the z-score in the table. That's the percent of the distribution less than your data. It's also the probability that fewer than 7200 people will show up.

(b) Compute the score for x = 8900. Look up the value of the z-score in the z-score table. That's the percent of the distribution less than 8900. You want MORE THAN 8900, so subtract the value from 1 toget the probability that more than 8900 people will show up.

(c) Subtract the percent you got from the z-score table for 7200 from the percent you got from the z-score table for 8900.