normal distribution question

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

The easiest way to approach this is to use the graphing calculator. In the graphing calculator (TI-83, 84, etc.) select [2nd] + [VARS], then choose option [2]: normalcdf

This allows you to find the percent (and probability) of the data found between two points on the normal distribution curve. The format looks like this:

normalcdf (a, b, x, y)

a = lower bound of the curve (if this has no lower bound, just enter a really small number like -10000000)

b = upper bound of the curve (if this has no upper bound, just enter a really big number like 10000000)

x = the mean of the data (provided)

y = the standard deviation of the data (provided)

So for a.) I would enter the below into the calculator: normalcdf(-100000, 7200, 7900, 500), and the calculator would return a value of 0.0807567112, which rounds to 0.0808, or approximately an 8.08% probability of a randomly selected day having attendance less than 7,200 people.

Based on this, you can calculate parts (b) and (c).