STA101 – Statistics for Business | Complete Solution

Instructions:

1.    Students are required to cover all stated requirements.
2.    Your answer must be both uploaded to Moodle in word file and handed over a printed copy.
3.    You need to support your answers with appropriate Harvard style references where necessary.
4.    Include a title/cover page containing the subject title and code and the name, student id numbers.
5.    Please save the document as STA101AT1_first name_Surename_Student Number
Question 1: (9 Marks)
Make a frequency distribution and histogram (using appropriate bins) for these 28 observations on the amount spent for dinner for four in downtown Chicago on Friday night. (b) Repeat the exercise, using a different number of bins. Which is preferred? Why? Dinner

95    103    109    170    114    113    107
124    105     80    104    84    176    115
69     95    134    108     61    160    128
68     95     61    150     52     87    136

Question 2: (8 marks)
On the midnight shift, the number of patients with head trauma in an emergency room has the probability distribution shown below. (a) FindP(X ≥ 3). (b) Find P(X ≤ 2). (c) Find P(X <, 4). (d) Find P(X = 1). (e) Which of the probability expressions in parts (a)–(d) is a value of the CDF?

x    0    1    2    3    4    5    Total
P(x)    .05    .30    .25    .20    .15    .05    1.00

Question 3: (6 marks)
Prof. Hardtack gave four Friday quizzes last semester in his 10-student senior tax accounting class.
a)    Find the mean, median, and mode for each quiz.
b)    Do these measures of center agree? Explain.
c)    For each data set, note strengths or weaknesses of each statistic of center.
d)    Are the data symmetric or skewed? If skewed, which direction?
e)    Briefly describe and compare student performance on each quiz.
Quizzes:
•    Quiz 1: 60, 60, 60, 60, 71, 73, 74, 75, 88, 99
•    Quiz 2: 65, 65, 65, 65, 70, 74, 79, 79, 79, 79
•    Quiz 3: 66, 67, 70, 71, 72, 72, 74, 74, 95, 99
•    Quiz 4: 10, 49, 70, 80, 85, 88, 90, 93, 97, 98

Question 4: (8 Marks)
Let S be the event that a randomly chosen female aged 18–24 is a smoker. Let C be the event that a randomly chosen female aged 18–24 is a Caucasian. Given P(S) = .246, P(C) = .830, and P(S ⋂C) = .232, find each probability.
a.    P(S′).
b.    P(S ⋃ C).
c.    P(S | C).
d.    P(S | C′).

Question 5: (9 marks)
Discuss why you would or would not expect each of the following variables to be normally distributed. Hint: Would you expect a single central mode and tapering tails? Would the distribution be roughly symmetric? Would one tail be longer than the other?
a.    Shoe sizes of adult males.
b.    Years of higher education of 30-year-old employed women.
c.    Days from mailing home utility bills to receipt of payment.
d.    Time to process insurance claims for residential fire damage.