Dr. H. Friedman

Midterm Review II

(1) A researcher wants to determine the average wage of American steel workers. A sample of 12 workers was selected randomly and indicated the following wages:
$20, $14, $10, $11, $12, $40, $30, $21, $22, $20, $20, $20.
(A) Calculate: The mean, median, Q1, Q3, mode, range, IQR, standard deviation, variance, and the coefficient of variation. (B) Standardize the $40 (i.e., convert the $40 into a z-score):

(2) The following is a frequency distribution showing the hourly wages of a sample of coal workers:

(A) Calculate the mean, median, Q1, Q3, mode, and range.

(3) There are 18 people. (A) How many ways can you assign them to 18 different jobs? (B) How many ways can you assign them to 3 different jobs? (C ) How many committees of 3 can you create from the 18 people?

(4) The probability of a computer being a Compaq is 15% . A company has 26 computers, what is the probability that 7 are Compaqs?

(5) A machine has 280 parts. The probability that any part is defective is .01. What is the probability that the machine works, i.e., 0 defective parts? Assume independence among the parts. (B) What is the probability that the machine does not work?

(6) A study of tattoos and crime found the following relationship:

(A) Compute these probabilities: P(C and T) ; P(C); P(C/T); P(C/T'); P(C or T). (B) Prove that tattoos and criminal records are not independent.

(7) The average wage of plumbers is normally distributed with a mean of $20 and a standard deviation of $5.50. Calculate the following:
(A) The proportion of plumbers earning between $18 and $22.
(B) The proportion of plumbers earning more than $28.
(C) The proportion of plumbers earning less than $15.
(D) Compute the 70th Percentile.

Answers:
(1) mean=$20, median=$20, Q1=$13, Q3=$21.50, mode=$20, range=$30, IQR=$8.50, S.D.=$8.45, C.V.=42.25%, Z-score for $40 is 2.37
(2) mean=$15.50, median=$15, Q1=$12, Q3=$18, mode=$15, range=$15.
(3) (A) 18! (B) 18P3=4,896 (C ) 18C3=816. (4) .051 (5) 6% that it works and 94% that it does not work.
(6) (A) P(C and T)=.05 ; P(C)= .27; P(C/T)=.50; P(C/T')= .244; P(C or T) =.32. (B) since P( C), P(C/T), and P(C/T') are not equal. Indeed, 50% of those with tattoos have criminal records vs. 24.4% without.
(7) (A) 28.12% (B) 7.35% (C ) 18.14% (D) $22.86

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