Statistics - Need some assistance with probability

Question

On a scale of 0 to 100 the average score for consumers (in a grocery store) with a child on their arms to buy candy is 

 

59. Assume that the standard deviation of the average score is 5. Also assume that the distribution is approximately

normally distributed.

 

What is the probability that a consumer has a choice score of…

a. More than 60?

b. Less than 80?

c. Between 70 and 85?

 

How do I go about computing this? Manually...? On Excel? 

 

Thank you in advance. 

d. Between 50 and 62?

Answer 1

This is a standard normal distribution question.  You need to calculate a z-score.  z=(x - μ)/σ .  Where, x is the number you are testing, µ=59 and σ=5.  You then have to look up the z-score in the z-table and interpret the corresponding values.  

 

For example, problem a. is setup as follows:  z = (60-59)/5 = 0.2  .  From a z-table this yields a probability of 0.4207 or 42.1% chance that the choice score is 60 or greater.