Question

***Just need question c answered ***

1. Use the following raw data to answer parts a and b of this question:

X_i: 3, 7, 14, 6, 17, 8, 10, 5

a. Calculate the mean, standard deviation, and variance for the above set of scores. Assume that the eight scores represent an entire population, and further assume that the scores are normally distributed.

b. Calculate the Z-score associated with each raw score.

c. Find the percentile scores which correspond to percentile ranks of 25%, 50%, and 90%, using the Z-score table and the formula to transform Z-scores into raw scores.

Answer 1

A)

Mean = (sum of the observations)/(number of observations)

Mean = (3+7....)/(8) = 8.75

To find variance

First we need to subtract mean from each and every observation and then we need to take the square and add them

= (3-8.75)^2 + (7-8.75)^2...

= 155.5

Variance = 155.5/8 = 19.4375

Standard deviation = √variance = √19.4375 = 4.41

Now you need c

C)

As the data is normally distributed

We can use z table

From z table, P(z<-0.67) = 25%

-0.67) = (x - mean)/s.s

X = 5.7953

25th percentile = 5.7953

From z table, P(z<0) = 50%

So, 0 = (x - 8.75)/4.41

X = 8.75

50th percentile = 8.75

From z table, P(z<1.28) = 90%

1.28 = (x - 8.75)/4.41

X = 14.3948

90th percentile = 14.3948