For a sample, M = 40. If X = 33.5 and the corresponding z = -1.2, calculate the

ID: 3208206 • Letter: F

Question

For a sample, M = 40. If X = 33.5 and the corresponding z = -1.2, calculate the variance. (2) Maya got a 65 in English. The average grade in her English class was 58, with sigma = 1. Maya also got a 78 in Chemistry, where the average grade was 77, with sigma = 0.5. Relative to everyone else in her classes, did Maya do better in her English or in her Chemistry class? Prove your claim by showing your work (i.e., don't just pick a class). (5) In general, why is it useful to transform every X value in a distribution into a corresponding z-score? (1) In doing this type of transformation, what happens to the shape of the distribution? (1) In doing this type of transformation, what happens to the mean (1) and the standard deviation (1)? Is a z-score of +1.43 above or below the mean? (1) How far is it from the mean? (1) Is this considered to be a typical or an extreme value? (1)

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Answere:

8a) z is given by the formula:

Z=(X-mean)/standard deviation

So, from our quetion we can write:

-1.2=(33.4-40)/standard deviation

which implies:

Standard deviation=5.5

So the variance is given by 5.5^2= 30.25

9. Maya had did better in Chemistry as

for English the z-score of Maya is (65-58)/1=7 that is Maya's score in English is 7 standard deviation away form the mean score in English.

whereas for Chemistry the z-score of Maya is (78-77)/0.5=2 that is Maya's score in Chemistry is just 2 standard deviation away from the mean score in Chemistry.

10. a)Tranfroming all the variables of a distribution to Z score give rise to a standard normal distributon. Also z score give an overall comparative view whether the variable is below average or above average and howmuch is the deviation.

b) The distribution becomes bell-shaped and it is symmetric about 0.

c) In doing this type of transformation the mean of the distribution becomes 0 and the standard deviations becomes 1.

d) +1.43 z-score is above mean. It is 1.43 standard deviation away from the mean. It is considered to be a typical value.

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For a sample, M = 40. If X = 33.5 and the corresponding z = -1.2, calculate the

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