30 September, 09:32

# 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?

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1. 30 September, 10:57
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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