Question

# Consider a sample with data values of 27, 25, 23, 16, 30, 33, 28, and 25....

Consider a sample with data values of 27, 25, 23, 16, 30, 33, 28, and 25. Compute the 20th ,25th ,65th ,75th percentiles (to 2 decimal, if decimals are necessary).

 20th percentile 25th percentile 65th percentile 75th percentile

Consider a sample with data values of 26, 25, 23, 15, 30, 36, 29, and 25. Compute the range, interquartile range, variance, and standard deviation (Round to 2 decimals, if necessary).

 Range Interquartile range Variance Standard deviation

Consider a sample with a mean of 60 and a standard deviation of 4 . Use Chebyshev's theorem to determine the percentage of the data within each of the following ranges (to the nearest whole number).

a. 50 to 70 , at least ____%

b. 35 to 85, at least _____%

c. 52 to 68 , at least ____%

d. 48 to 72 , at least _____%

e. 44 to 76, at least _____%

The results of a national survey showed that on average, adults sleep 6.9 hours per night. Suppose that the standard deviation is 1.4 hours. Round your answers to the nearest whole number.

a. Use Chebyshev's theorem to calculate the percentage of individuals who sleep between 4.1 and 9.7 hours.

At least ______%

b. Use Chebyshev's theorem to calculate the percentage of individuals who sleep between 3.9 and 9.9 hours.

At least ______%

c. Assume that the number of hours of sleep follows a bell-shaped distribution. Use the empirical rule to calculate the percentage of individuals who sleep between 4.1 and 9.7 hours per day.

At least _______%

How does this result compare to the value that you obtained using Chebyshev's theorem?

- Select your answer -The empirical rule produces a larger percentage than Chebyshev's theorem; Chebyshev's theorem produces a larger percentage than the empirical rule; Both methods produce the same percentage

Many families in California are using backyard structures for home offices, art studios, and hobby areas as well as for additional storage. Suppose that the mean price for a customized wooden, shingled backyard structure is . Assume that the standard deviation is .

a. What is the  -score for a backyard structure costing  (to 2 decimals)? If your answer is negative, enter minus (-) sign.

b. What is the  -score for a backyard structure costing  (to 2 decimals)?

c. Interpret the  -scores in parts (a) and (b). Comment on whether either should be considered an outlier.

- Select your answer -The z -score in part (a) is an outlierThe z -score in part (b) is an outlierBoth are outliersNeither is an outlierItem 7

d. If the cost for a backyard shed-office combination built in Albany, California, is , should this structure be considered an outlier? Explain.

is    (to 2 decimals) standard deviations  - Select your answer -abovebelowItem 9 the mean. This cost  - Select your answer -isis notItem 10 an outlier.

1)

 27 25 23 16 30 33 28 25 20 23.8 25 24.5 65 27.55 75 28.5

use =percentile(array,k) in excel

k = 0.2,0.25 etc

2)

 26 25 23 15 30 36 29 25 Range 21 Interquartile range 4.75 Variance 36.6964286 Standard deviation 6.05775772

formulas

 26 25 23 15 30 36 29 25 Range =MAX(B1:B8) - MIN(B1:B8) Interquartile range =QUARTILE(B1:B8,3) - QUARTILE(B1:B8,1) Variance =VAR(B1:B8) Standard deviation =SQRT(B12)

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