Given a normal distribution with ? = 100 and ? = 10,...

Given a normal distribution with ? = 100 and ? = 10, complete parts (a) through (d). a. What is the probability that X > 70? The probability that X > 70 is 0.9986 . (Round to four decimal places as needed.) b. What is the probability that X < 80? The probability that X < 80 is 0.0227 . (Round to four decimal places as needed.) c. What is the probability that X < 75 or X > 115? The probability that X < 75 or X > 115 is 0.0730 . (Round to four decimal places as needed.) d. 99% of the values are between what two X-values (symmetrically distributed around the mean)? 99% of the values are greater than and less than . (Round to two decimal places as needed.)

Transcript

00:01 There is given a normal distribution for this question.

00:03 So the main value was given here, which is denoted by mode.

00:06 This is 100.

00:08 And the standard deviation, denoted by sigma, and that was given as 10 here.

00:14 So we have to just define the random variable x.

00:17 This is normally distributed.

00:18 So this is 110.

00:20 So for the first part of the question, we have to find the probability of the random variable x, which is greater than 70.

00:26 To get this parallel, i'm going to use the graph in display calculator application, the normal cdf.

00:32 So the lower boundary is 17, no upper boundary put very big number, and the mean is 100 and the standard division 10, which is press second variance, the second option.

00:42 So the lower boundary is 70, the upper boundary is one, this is second e99, and the mean is 100 and the standard division 10.

00:51 So the answer would be which is 0 .99 and 807.

00:55 This is the probability here.

00:59 And the next one, which is the probability of random variable x, sorry, this is random variable x, which is less than 80.

01:06 So at this step, again, i'm going to use the normal cdf.

01:10 So there is no lower boundary, put a very small number, the upper boundary 80.

01:14 So the mean and the standard deviation, which is press second variance, the second option, this is negative one, second e99.

01:22 The upper boundary is 80, and the mean is 100 and the standard division 10.

01:27 So the answer would be which is 0 .02 and 28.

01:33 And for c, the probability for this one, which is between, so this is x is less than 75 or the x is greater than 115.

01:45 So i can find this area which is the total probability minus, the excluded part, where the x value is between 115 and greater than 75.

01:54 To get this probability, again, i'm going to use the normal cdf...

Question

Please give Ace some feedback