Question

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.

is standard deviations - Select your answer -belowaboveItem 4 the mean.

is standard deviations - Select your answer -belowaboveItem 6 the mean.

- 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.

Answer #1

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) |

Consider a sample with data values of 27, 24, 19, 14, 30, 33,
28, and 24. Compute the 20th, 25th, 65th, and 75th percentiles
20th percentile
25th percentile
65th percentile
75th percentile

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 3000. Assume that the
standard deviation is 1100.
a. What is the -score for a backyard structure costing 2300 (to
2 decimals)? If your answer is negative, enter minus (-) sign.
b. What is the -score for a backyard structure costing 4800 (to
2 decimals)?...

Consider a sample with a mean of 30 and a standard deviation of
6. Use Chebyshev's theorem to determine the percentage of the data
within each of the following ranges(to the nearest whole
number).
a) 10 to 50, at least ____%
b)15 to 45, at least ___%
c) 22 to 38, at least ___%
d) 17 to 43, at least ___%
e) 14 to 46, at least ___%

11.
Using the accompanying table of data, blood platelet counts of
women have a bell-shaped distribution with a mean of 255.0 and a
standard deviation of 65.5
(All units are 1000 cells/μL.)
Using Chebyshev's theorem, what is known about the percentage
of women with platelet counts that are within 2 standard deviations
of the mean? What are the minimum and maximum possible platelet
counts that are within 2 standard deviations of the mean?
At least how many % of women...

A sample of men's ages at first marriage is below.
26
31
29
27
30
28
27
31
23
29
29
30
32
28
30
28
29
35
a) Calculate x¯_______ and_______ s to 03 decimal places.
x¯= and s=
b) Calculate the intervals x¯±s, x¯±2s, and x¯±3s
using the values from a).
x¯±s= _______to _________
x¯±2s= ________to _________
x¯±3s= _______to ________
c) What proportion of values fall within each interval? How does
this compare to the Empirical Guidelines?
Round your...

BIG Corporation produces just about everything but is currently
interested in the lifetimes of its batteries, hoping to obtain its
share of a market boosted by the popularity of portable CD and MP3
players. To investigate its new line of Ultra batteries, BIG
randomly selects 1000 Ultra batteries and finds that they have a
mean lifetime of 834 hours, with a standard deviation of 81 hours.
Suppose that this mean and standard deviation apply to the
population of all Ultra...

A sample of 124124 motels is selected from a large urban area
and the price for a night of lodging for a single room was
determined for each motel. The mean rate is computed to be $89$89
and the standard deviation is $15$15. One motel charged $57$57
per night which is the 15th percentile. Another motel
charged $121$121 per night which is the 75th
percentile.
Step 2 of 5:
How many motels charged $121$121 or less per night? Round your...

Consider the following IQ data obtained from a sample of 25
incarcerated youth. Convert the 25 raw adjustment scores to
standardized scores. Show work for at least one of the 25 scores.
(Hint: You need to calculate the mean and SD first!) (4pts
for entire column) *For this question, only TWO decimal
places are required.
ID: 1, 2, 3, 4, 5, 6 , 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17,
18, 19, 20, 21, 22, 23,...

1.) Calculate both the sample and the population standard
deviations using the data below.
x
14
20
26
18
6
24
Please show the following answers to 1 decimal
place.
Sample Standard Deviation (ss) =
Population Standard Deviation (σσ) =
Notice the different!
2.) The highway mileage (mpg) for a sample of 9 different models
of a car company can be found below.
20
27
35
49
35
43
22
28
40
Find the mode:
Find the midrange:
Find the...

Consider the following population data:
42
48
19
16
28
a. Calculate the range.
b. Calculate MAD. (Round your
intermediate calculations to at least 4 decimal places and final
answer to 2 decimal places.)
c. Calculate the population variance.
(Round your intermediate calculations to at least 4 decimal
places and final answer to 2 decimal places.)
d. Calculate the population standard deviation.
(Round your intermediate calculations to at least 4 decimal
places and final answer to 2 decimal places.)

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