1. The health insurance requires a minimum of 65 pts on the exam to pass. The exam standard deviation of 8.4 points and normal distribution has a mean of 72.1 pts.

a. Calculate the percentage of health insurance takers that pass the exam with 65 pts and above.

b. Calculate what pts cut off is the top 8% who passed the exam

Expert Solution

mean = 72.1 , sigma = 8.4

Using central limit theorem,

z = (x -mean)/sigma

P(x> 65)
= P(z> (65 - 72.1)/8.4)
= P(z> -0.85)
= 1- P(z< -0.85)
= 1 - 0.1990
= 0.8010

b)

the z value at top 8% = 1.41

z = (x -mean)/sigma

1.41 = (x - 72.1)/8.4

x = 1.41 * 8.4 + 72.1
x = 83.94

orchestra answered 2 years ago

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