1. NEED C ONLY! A sample of eight companies in the aerospace industry was survey

Question

1. NEED C ONLY!

A sample of eight companies in the aerospace industry was surveyed as to their return on investment last year. The results are (in percent): 10.6, 12.6, 14.8, 18.2, 12.0, 14.8, 12.2, and 15.6.

a) Range: 7.60

b) Arithmetic Mean: 13.85

c) Standard Deviation: (Round to 2 decimal places) ?

2. NEED B AND C ONLY!

A sample of 25 undergraduates reported the following dollar amounts of entertainment expenses last year:

a) Mean: $698.20 / Median: $724 / Mode: $682 and $700 / Range: 92

b) Standard Deviation: (Round to 2 decimal places): ?

c) Use the Empirical Rule to establish an interval which includes 95% of the observations: (Round to 2 decimal places)

The interval is from _____ up to _____ ?

A sample of 25 undergraduates reported the following dollar amounts of entertainment expenses last year:

Explanation / Answer

1) c part

First we can calculate the variance and then take square root of variance to get the standard deviation.

Here the sample of return of investments is given below:
10.6, 12.6, 14.8, 18.2, 12.0, 14.8, 12.2, and 15.6.

First we can calculate the variance as below:
Variance = (Sum of squares)/(N-1)

Here mean = 13.85

Variance = ((10.6 - 13.85)^2 + (12.6 - 13.85)^2 + (14.8 - 13.85)^2 + (18.2 - 13.85)^2 + (12 - 13.85)^2 + (14.8 - 13.85)^2 + (12.2 - 13.85)^2 + (15.6- 13.85)^2) /(8 - 1)

Variance = 6.008571

Standard deviation = sqrt(Variance) = 2.45

2. b part

Here the sample of entertainment expenses in dollars is as below:
766,712,737,700,680,772,721,689,697,759,725,750,714,724,744,682,682,755,731,699,757,711,760,700,770

First we can calculate the variance
Variance = (Sum of squares)/N-1

Variance = ((766 - 725.48)^2 + (712 - 725.48)^2 + (737 - 725.48)^2 + (700 - 725.48)^2 + (680 - 725.48)^2 + (772 - 725.48)^2 + (721 - 725.48)^2 + (689- 725.48)^2 + (697 - 725.48)^2 + (759 - 725.48)^2 + (725 - 725.48)^2 + (750 - 725.48)^2 + (714 - 725.48)^2 + (724 - 725.48)^2 + (744 - 725.48)^2 + (682- 725.48)^2 + (682- 725.48)^2 + (755- 725.48)^2+ (731- 725.48)^2+ (699- 725.48)^2+ (757- 725.48)^2+ (711- 725.48)^2+ (760- 725.48)^2+ (700- 725.48)^2+ (770- 725.48)^2) /(25 - 1)

Variance = 900.51

Standard deviation = sqrt(900.51) = 30.0085 = 30.01(round to 2 decimal places)

c) Empirical rule says that 95% of the data in normal distribution falls between 2 standard deviations of the mean.

So the interval is from (mean - 2 * sd) to (mean + 2*sd)

So the interval is from (725.48 - 2 * 30.01) to (725.48 + 2 * 30.01)

So interval is 665.46 to 785.5

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