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
