Sat scores assume that in a given year the mean mathematics...

Name: sat scores assume that in a given year the mean mathematics sat score was 566 and the standard deviation was 126 a sample of 70 scores is chosen use the ti 84 plus calculatord using a cutoff 82256
Uploaded: 2022-11-01T11:55:15-08:00
Duration: 6 min 7 s
Channel: David Nguyen
Description: sat scores assume that in a given year the mean mathematics sat score was 566 and the standard deviation was 126 a sample of 70 scores is chosen use the ti 84 plus calculatord using a cutoff 82256

SAT scores: Assume that in a given year the mean mathematics SAT score was 566 , and the standard deviation was 126 . A sample of 70 scores is chosen. Use the TI-84 Plus calculator.(d) Using a cutoff of 0.05 ,would it be unusual if the sample mean were greater than 570 ? Round the answer to at least four decimal places. It ▼(Choose one) be unusual if the sample mean were greater than 570 , since the probability is

Transcript

00:01 Hi, i'm david and i'm here to help you understand your question.

00:03 Now let me pick up your question here.

00:06 Let me make it bigger.

00:09 In the question here we are going to discuss about the central limit theorem.

00:16 And the theorem says that if we have the n -quiet equal to the 30, then the sum of mean x -bow could be approximately to the normal.

00:23 In such a way that if we tell the x -bile remains the mean of a standard division devalued is going to end, we have 10 the standard normal.

00:30 In the question here we have the n equals to the 76, where we have the mean equal to the 600 and the sigma equal to the 135.

00:44 Now in the first question a, i'm going to find the probability that the sum will mean x bar will be less than the 590.

00:54 To find this probability, i need to convert the x bar here into the z.

00:58 To do it and apply this formula here and then we will get the 590 we minus the mean divided by the sigma over square number 76 and if we compute we have the z could be smaller than 590 minus 600 divided by 135 times square in the 76 equal to minus 0 upon 64 6 so using the we can find this probability it will equal to the minus 0 .646 then can equal to the 0 .2591 around to the 4 decimal places.

01:49 Now for the question b we want to find the probability that the symbol means x bar will be between the 5.

02:01 65 and the 604 again we can put that into the z and then we turn the 565 we minus the mean over 135 the square root 76 6 of 4 we minus the mean over the 135 the number square under the 76 and then we get the probability of the z will be between here 565 minus 600 divide 1 35 times square root under 76 equal to the minus 2 .26.

02:40 6 addition for the 155 times square minus 76 equal to the 0 .26 and then we go have this one will be 0 .26 and then get equal to the 016 -2 -57 minus the minus 2 .26, 0 .1191.

03:15 Then again equal to the 0 .59 .7...

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