Thread: Normal distribution question

I can't seem to be able to understand word problems

an applicant take a test . The time it normally distributed with mean time 60 minutes and standard deviation 8 minutes . Determine how much time an applicant should be given in general so 97 percent of them will be able to complete the test

First step back and think about it. The mean time is 60, and you want to find the time that 97% of folks take less than. "97%" corresponds to a little more than 2 standard deviations above the mean, right? [Why?]
So your answer will be a little less than 60 + 2 * 8 = 76...right?

Here's a hint on the details:

You want to find time T so that F(t) = prob(t < T) = 0.97.

We know


So you want to solve

for t.

We know


So you want to find t so that

Let “x” variable is normally distributed, represents the time.

µ=60 and σ=8 are the mean and standard deviation of the time.

So we have to find x1 where 97% students will be able to complete their test.

So,

z1 = (x1 - µ)/σ (z1 lies on z-axis corresponding x1 on x-axis)

x1=µ+z1σ
x1= 60+(1.88)(8) [z1 take from z-dist. Table]
x1= 75.04 ~75
x1= 75

So if the time will be 75 min, then the students will be able to complete their test 97% complete.