Question

b. Read the three problems listed below and determine: (1) what type of probability distribution would be used to solve each problem and why; (2) pick one problem from below and provide a detailed solution with an explanation; (3) indicate which problem you selected to solve in your subject line.

i. The reading speed of sixth-grade students is approximately normal, with a mean speed of 125 words per minute and a standard deviation of 24 words per minute. Find and interpret the probability that a randomly selected sixth-grade student reads less than 100 words per minute.

ii. A Wendy’s manager performed a study to determine a probability distribution for the number of people, X, waiting in a line during lunch. The results were as follows. Find and interpret the probability that 10 or more people are waiting in line for lunch?

Probability

x	P(x)	x	P(x)
0	0.011	7	0.098
1	0.035	8	0.063
2	0.089	9	0.035
3	0.150	10	0.019
4	0.186	11	0.004
5	0.172	12	0.006
6	0.132

iii. Clarinex-D is a medication whose purpose is to reduce the symptoms associated with a variety of allergies. In clinical trials of Clarinex-D, 5% of the patients in the study experienced insomnia as a side effect. As random sample of 20 Clarinex-D users is obtained, and the number of patients who experienced insomnia is recorded. Find and interpret probability that 3 or fewer experienced insomnia as a side effect.

Answer 1

Probability distribution used for each problem     
1)   Normal Distribution with μ = 125 and σ = 24     
2)   Discrete probability distribution     
3)   Binomial Distribution with n = 20 and p = 0.05     
      
Solving problem 1 in detail     
1) Let X be the reading speed of sixth grade student     
X ~ Normal Distribution with μ = 125 and σ = 24     
To find P(X < 100)     
We use Excel function NORM.DIST to find this probability     
P(X < 100) = NORM.DIST(100, 125, 24, TRUE)     
   = 0.1488    
P(sixth-grade student reads less than 100 wpm) = 0.1488