Question

The number of new theatre productions that appear on broadway are as follows: 30, 28, 33, 28, 37, 39, 35, 37, 38, 34 Formulas must be used and show all work

g. Find the s-score of 30 theatre productions

h. find the 90th percentile

i. Construct a boxplot and comment on shape of the distribution

Answer 1

Solution:

The z score formula is given as below:

Z = (X – mean) / SD

Mean = ∑X/n

Variance = ∑(X – mean)^2/(n – 1)

SD = sqrt(variance)

Calculation table is given as below:

No.	X	(X - mean)^2
1	30	15.21
2	28	34.81
3	33	0.81
4	28	34.81
5	37	9.61
6	39	26.01
7	35	1.21
8	37	9.61
9	38	16.81
10	34	0.01
Total	339	148.9
Mean	33.9

Mean = ∑X/n = 339/10 = 33.9

Variance = ∑(X – mean)^2/(n – 1) = 148.9/(10 – 1) = 16.54444444

SD = sqrt(variance) = sqrt(16.54444444) = 4.067486256

Part g

Z score for X = 30

Z = (X – mean) / SD

Z = (30 - 33.9) / 4.067486256

Z = -0.95882

Part h

90^th percentile = Mean + Z*SD

Z = 1.281552

(by using z-table)

90^th percentile = 33.9 + 1.281552*4.067486256

90^th percentile = 39.1127

Part i

The required box plot is given as below:

Boxplot 25 35

From above box plot, it is observed that the given data is skewed at left side.