given a normal distribution with 50 and 6 3 complete parts a through d click here to view page 1

Step 1: To find the probability that X > 45, we need to find the area under the normal curve to

Given a normal distribution with 50 and 6 3 complete parts a...

Given a normal distribution with µ = 50 and 6 = 3, complete parts (a) through (d). Click here to view page 1 of the cumulative standardized normal distribution table. Click here to view page 2 of the cumulative standardized normal distribution table. a. What is the probability that X > 45? P(X>45)= 0.515 (Round to four decimal places as needed.) b. What is the probability that X < 44? P(X<44) = 0.0217 (Round to four decimal places as needed.) c. For this distribution, 9% of the values are less than what X-value? X= (Round to the nearest integer as needed.) d. Between what two X-values (symmetrically distributed around the mean) are 60% of the values? For this distribution, 60% of the values are between X = and X = (Round to the nearest integer as needed.)

Transcript

00:01 There is given a normal distribution, the mean, which is denoted by mu, that was given as 49, and the standard deviation denoted by sigma.

00:12 That was given as 3.

00:14 And i can define the random variable x for this population distribution.

00:18 The mean is 49 and the standard division, which is 3.

00:23 Let's try to get the first part of the answer.

00:25 What is the probability? so the probability of random variable x, which is greater than 45, i can use.

00:31 Use the normal cdf function here what am i supposed to put the lower boundary for the 5 there is no in upper boundary i can put very small they're very big number the mean was 49 and the standard division is 3 let's get the answer so i'm going to just find the normal cdf press second variance the second option here lower boundary 45 the upper boundary is 1 the second 899 and the mean is 49 and the standard division which is 3 so the answer would be this is 0 .0.

01:01 90 and then 88.

01:06 This is the answer we have for the first part of this question here.

01:12 And what about for the next part? let's say this is b.

01:17 And the probability of x, so the probability of x is less than 43.

01:23 Again, i'm going to use the normal cdf here, the lower boundary, negative 1e99, the upper boundary is 43, the mean and the standard division, which is equal.

01:34 To so again press second variance the second option lower boundary and the upper boundary the mean in the standard division so the answer is 0 .0 2 2 and 8 this is 0 .0 2 2 and 8 and what about for part c let's say x1 be the value so if the 6 % are less than this x value so i can just graph the distribution here.

02:10 This is the normal distribution we have.

02:11 The 6 % is less than 50%.

02:14 There should be some x1 here and the area of this region, which is 6%, which is written as 0 .06.

02:21 In order to get the x1, we know that the random variable x is less than x1, which is 0 .06.

02:27 So i'm going to use the inverse normal function.

02:30 And from left to right, the area was 0 .06.

02:33 And the mean value for this distribution, this is 49 and the standard division is 3...