Question

1. a sample of production records for an automobile manufacturer shows the following figures for production per shift.

705 700 690 705
what is the standard deviation of this sample?
a. 8.66
b. 7.07
c. 20
d. 50
e. 75

1. a lobster fisherman is keeping track of the productivity of a set of traps he has placed in a favorite location. below are the numbers of lobsters in these traps over the course of 12 different hauls.

0 3 3 3 4 5 5 6 7 7 12 14
according to the 1.5 × iqr outlier rule, which values are outliers?
a. 0 only
b. 14 only
c. 12 and 14
d. 0 and 14
e. 0, 12, and 14

1. carrie and vicki are both enthusiastic players of a certain computer game. over the past year, carrie’s mean score when playing the game is 12,400 with a standard deviation of 1500. during the same period, vicki’s mean score is 14,200, with a standard deviation of 2000. they devise a fair contest: each one will play the game once, and they will compare z - scores. carrie gets a score of 14,000, and vicki gets a score of 16,000. calculate their z - scores and determine who won the contest.

a. carrie’s z = 1.07; vicki’s z = 1.11; vicki wins the contest.
b. carrie’s z = 1.07; vicki’s z = 0.90; carrie wins the contest.
c. carrie’s z = 0.94; vicki’s z = 1.11; vicki wins the contest.
d. carrie’s z = 0.94; vicki’s z = 0.90; carrie wins the contest.
e. carrie’s z = 0.81; vicki’s z = 0.99; vicki wins the contest.

1. a sample was taken of the salaries of 20 employees of a large company. the following are the salaries (in thousands of dollars) for this year.

28 31 34 35 37 41 42 42 42 47
49 51 52 52 60 61 67 72 75 77
suppose each employee in the company receives a $3,000 raise for next year (each employee’s salary is increased by $3,000). the standard deviation of the salaries for the employees will
a. be unchanged.
b. increase by $3,000.
c. be multiplied by $3,000.
d. increase by \\(\sqrt{3000}\\).
e. decrease by $3,000.

Explanation:

Question 4

Step1: Calculate sample mean

$\bar{x} = \frac{705 + 700 + 690 + 705}{4} = \frac{2800}{4} = 700$

Step2: Compute squared deviations

$(705-700)^2 + (700-700)^2 + (690-700)^2 + (705-700)^2 = 25 + 0 + 100 + 25 = 150$

Step3: Calculate sample variance

$s^2 = \frac{150}{4-1} = 50$

Step4: Find sample standard deviation

$s = \sqrt{50} \approx 7.07$

Step1: Find median, Q1, Q3

Data sorted: 0,3,3,3,4,5,5,6,7,7,12,14
Median = $\frac{5+5}{2}=5$; Q1 = 3; Q3 = 7

Step2: Calculate IQR

$IQR = Q3 - Q1 = 7 - 3 = 4$

Step3: Set outlier bounds

Lower bound: $Q1 - 1.5\times IQR = 3 - 6 = -3$
Upper bound: $Q3 + 1.5\times IQR = 7 + 6 = 13$

Step4: Identify outliers

Values outside bounds: 14

Step1: Calculate Carrie's z-score

$z = \frac{x-\mu}{\sigma} = \frac{14000-12400}{1500} = \frac{1600}{1500} \approx 1.07$

Step2: Calculate Vicki's z-score

$z = \frac{x-\mu}{\sigma} = \frac{16000-14200}{2000} = \frac{1800}{2000} = 0.90$

Step3: Compare z-scores

Carrie's z-score is higher, so she wins.

Answer:

b. 7.07

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Question 5