SOLUTION: The purchases made by customers at a convenience store are normally distributed, with a mean of $8.50 and a standard deviation of $6.00. What is the probability that a randomly cho

Algebra ->  Probability-and-statistics -> SOLUTION: The purchases made by customers at a convenience store are normally distributed, with a mean of $8.50 and a standard deviation of $6.00. What is the probability that a randomly cho      Log On


   

Question 872649: The purchases made by customers at a convenience store are normally distributed, with a mean of $8.50 and a standard deviation of $6.00. What is the probability that a randomly chosen customer makes a purchase between $2.50 and $14.50?
Thank you very much!
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

mean of $8.50 and a >standard deviation of $6.00

P($2.50 ≤ x ≤ $14.50) = P(-1 ≤ z ≤ 1) = .8413 -.1587 = .6826  0r 68.26%



For the normal distribution: 

one  standard deviation from the mean accounts for about 68% of the set 

two standard deviations from the mean account for about 95%

and three standard deviations from the mean account for about 99.7%.



Important to Understand z -values as they relate to the Standard Normal curve:

Below:  z = 0, z = ± 1, z= ±2 , z= ±3 are plotted.  

Note: z = 0 (where the x-value is the mean)

 50% of the area under the curve is to the left and %50 to the right