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Assignmentz (20%)
Assignmentz (20%)
(1) Find the proportion For:
a. Between the mean and Z= +2.40 bi Between Z = +1.50 and Z= +2.45 (C) Between Z= -1.25 and 2= +3.20 2= +0.99?

Mar 1

Assignmentz (20%)

(1) Find the proportion For:

a. Between the mean and Z= +2.40 bi Between Z = +1.50 and Z= +2.45 (C) Between Z= -1.25 and 2= +3.20 2= +0.99

(d) Beloo

(e) Above Z= -1.60

(2) A student has a score 25 on a quit with a mean of 20 and 6=5 and she has also scored 56 on Final exam With pl = 68 and 6=12, on which test she Scores better? (3) A normal distribution has μl = 10 and 0 = 1, what is the z-score cutoff for the top and bottom 2:15% of the distribution?

(4) IQ Score are normally distributed with H=100

and 0=15.

(a) what proportion of scores would be between scores 65

and

go?

(b) what proportion of Scores would be above score 125? (c) What Score would be at the 70th percentile? (d) What score. cutoff the top 10% of the distribution? (e) If 200 Students took the IQ test, howmaney students

Will Score less than Score 80?

(f) If the top 1% are to be given Scholarship, what will be the cutoff (pass mark) for the scholarship? (5) Anormal distribution has a mean of 40 and Standard deviation of 6. What Values are the top 20% of the data?

NB. Show all the Steps while working out!)

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Mar 1

To find the proportion between two Z-scores, we need to use a standard normal distribution table or a calculator that can calculate the area under the standard normal curve.

a. Between Z = +1.50 and Z = +2.45:

Using a standard normal distribution table or calculator, we find the area to the left of Z = +1.50 is 0.9332 and the area to the left of Z = +2.45 is 0.9929. Therefore, the proportion between Z = +1.50 and Z = +2.45 is:

0.9929 - 0.9332 = 0.0597

b. Between Z = -1.25 and Z = +3.20:

Using a standard normal distribution table or calculator, we find the area to the left of Z = -1.25 is 0.1056 and the area to the left of Z = +3.20 is 0.9993. Therefore, the proportion between Z = -1.25 and Z = +3.20 is:

0.9993 - 0.1056 = 0.8937

c. Between Z = 0 and Z = +0.99:

Using a standard normal distribution table or calculator, we find the area to the left of Z = 0 is 0.5000 and the area to the left of Z = +0.99 is 0.8389. Therefore, the proportion between Z = 0 and Z = +0.99 is:

0.8389 - 0.5000 = 0.3389

Therefore, the proportions for the given Z-score ranges are:

a. 0.0597

b. 0.8937

c. 0.3389

a. Between Z = +1.50 and Z = +2.45:

Using a standard normal distribution table or calculator, we find the area to the left of Z = +1.50 is 0.9332 and the area to the left of Z = +2.45 is 0.9929. Therefore, the proportion between Z = +1.50 and Z = +2.45 is:

0.9929 - 0.9332 = 0.0597

b. Between Z = -1.25 and Z = +3.20:

Using a standard normal distribution table or calculator, we find the area to the left of Z = -1.25 is 0.1056 and the area to the left of Z = +3.20 is 0.9993. Therefore, the proportion between Z = -1.25 and Z = +3.20 is:

0.9993 - 0.1056 = 0.8937

c. Between Z = 0 and Z = +0.99:

Using a standard normal distribution table or calculator, we find the area to the left of Z = 0 is 0.5000 and the area to the left of Z = +0.99 is 0.8389. Therefore, the proportion between Z = 0 and Z = +0.99 is:

0.8389 - 0.5000 = 0.3389

Therefore, the proportions for the given Z-score ranges are:

a. 0.0597

b. 0.8937

c. 0.3389