The time needed to complete a final examination in a...

The time needed to complete a final examination in a particular college course is normally distributed with a mean of 80 minutes and a standard deviation of 10 minutes. Answer the following questions. a. What is the probability of completing the exam in one hour or less? b. What is the probability that a student will complete the exam in more than 60 minutes but less than 75 minutes? c. Assume that the class has 60 students and that the examination period is 90 minutes in length. How many students do you expect will be unable to complete the exam in the allotted time?

Transcript

00:01 There is given a normal distribution here.

00:03 The mean value was given here.

00:04 So the mean denoted by minute, this is 80 minutes.

00:08 So the unit here, which is minutes.

00:11 And the standard deviation is 10.

00:13 So the standard deviation denoted by sigma, which is 10 minutes.

00:19 So since it's a normal distribution, i can define the random variable x here.

00:23 This is normally distributed, which is 80 and 10.

00:26 Let's take a look at the first part.

00:28 So the probability completing the exam in 1r.

00:32 So the 1r is 60 minutes.

00:34 So first of all, the 1r, which is equal to 60 minutes.

00:37 So we can just find the random variable x, which is less than a equal to 60.

00:43 In order to find this probability, i'm going to use the normal cdf function.

00:46 The lower boundary that goes to negative infinity.

00:49 The upper boundary here is 60, and the main value is 80, and this standard division is 10.

00:54 Let's get the answer.

00:55 There's a second variance, the normal cdf, the second option here.

00:58 Lower boundary that is negative 1 second a 99 the upper boundary is 60 and the mean is 80 in the standard division which is 10 so the probability here is 0 .02 and then 28 this is the probability we have for this case and what about for b this is more than 60 minutes but less than 75 so that means the random variable x which is less than 75 and more than 60 so again i'm going to use the normal cdf, the lower boundary is 60, upper boundary is 75, the mean is 80 and the standard division is 10.

01:37 Press second variance, the second option here, the lower boundary, 60, the upper boundary is 75 and the mean is 80 and the standard division which is 10.

01:46 Let's get the answer.

01:47 This is 0 .28 and then 58.

01:51 And what about for part c? so for part c, so there is a clause 60, so that so there's given a sample here so the sample size is 60 and we have the just examination period which is 90 minutes how many students do you expect will be unable to complete the exam in the allotted time so first of all we have to just find the random variable x is greater than 90 give us the probability of people who doesn't who don't just complete the exam in allotted allocated time so in order to get this i'm going to use the normal cdf...

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