Question

The time taken by a randomly selected applicant for a mortgage to fill out a certain form has a normal distribution with mean value 10 min and standard deviation 2 min. if five individuals fill out a form on one day and six on another, what is the probability that the sample average amount of time taken on each day is at most 11 min?

Answer 1

To solve for the probability proportion, we make use of the z statistic. The procedure to do is to calculate for the z value and using the standard probability tables, we can look up for the p value. The formula for z score is:

z =(x – μ) / (σ / sqrt(n))

where,

x = sample score = 11

μ = sample mean= 10

σ = standard deviation = 2

n = sample size

 

Calculating for the z and p value when n = 5:

z =(11 – 10) / (2 / sqrt(5))

z = 1.12

Using the tables, p(5) = 0.8686

 

Calculating for the z and p value when n = 6:

z =(11 – 10) / (2 / sqrt(6))

z = 1.22

Using the tables, p(6) = 0.8888

 

If both days should be occuring, therefore the total probability that each day is at most 11 min is:

p total = p(5) * p(6)

p total = 0.8686 * 0.8888

p total = 0.772