Question 4 15 points the intelligence quotient iq test...

Question 4: (15 points) The Intelligence Quotient (IQ) test scores for adults are normally distributed with a population mean of 100 and a population standard deviation of 15. (i) What is the probability we could select a sample of 50 adults and find the mean score of this sample is less than 95? (ii) What is the probability we could select a sample of 50 adults and find the mean score of this sample is between 94 and 106?

Transcript

00:01 So our question says that the intelligence quotient.

00:09 Our question says that the iq test scores for adults are normally distributed with a population mean of 100 and a population standard division of 15.

00:18 So the first question says that what is the probability that we could select a sample of 50 adults and find the mean score of this sample is less than 95.

00:27 So let's get that.

00:30 Our m u is equal to 100 sigma we have that to be equals to 15 our n is equal to we have the n to be cost to 50 and we are supposed to get probability that x is less than 95 so to get this probabilistic value we are going to standardize a random variable x into a z score by using the formal that says z is equals to x minus md divided by zx divided by zx square out of ed x in this case of us is 95 minus 100 divided by 15 divided by the square out of 50 so we have minus 5 divided by so 15 divided by square out of 50 we have our answer to be 2 .1213 so when we do the maths minus 5 whereby 2 .1213 our answer is minus 2 .36 so that's in implies a probability that x is less than 95 is same thing as probability that z is less than minus 2 .36 so i'll be using a calculator to get this value so here's my calculator over here we have a left tail test we have a z score and this is minus 2 .36 and our answer is 0 .091 rather here is the probability that at the mean score of this sample of this sample going to be less than 95 is actually 0 .0091.

02:07 Our second question says that the same question, what is the probability that we could select a sample of 50 adults and find the mean score of the sample to be between 94 and 1006.

02:18 So the same question but we are having our sample mean to be between 94.

02:25 So in this case of us, we are having two random variables value.

02:29 We have 94 and we have 1006.

02:31 So we standardize each of them...

Question

Please give Ace some feedback