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Business Data Analysis Questions Essay Example
 Category:Finance & Accounting
 Document type:Math Problem
 Level:Undergraduate
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BUSINESS DATA ANALYSIS7
Business Data Analysis
Question One

D. reason 1.1 is not a valid probability.
Probabilities space range from 0 to 1
0 ≤ P (A) ≥ 1

Mean of probability distribution is C.
Reason
The sum of the variable X and P(X)
From the distribution
= 0 x 0.2 + 1 x 0.4 + 2 x 0.3 + 3 x 0.1
= 0 + 0.4 + 0.6 + 0.3
= 1.3

To get the variance
We square the variable X and multiply the result with P(x), we subtract the square of the mean from the result and then get a square root
= 0^{2}(0.2) + 1^{2}(0.4) + 2^{2}(0.3) + 3^{2}(0.1)
= 0 + 0.4 + 1.2 + 0.9
= 2.5
= 2.5 – 1.3^{2}
= 2.5 – 1.69
= 0.81
= 0.9 (A is the correct answer)

P(Z>1.48)
1 — P (Z<= 1.48)
1 – 0.9306
0.0694

P(X>5) = 0.4

The probability of getting one four is
=1/6 x 1/6
= 1/36

P(A) = 0.2 and P(B) = 0.3
The P (A and B) = P (A) P (B)
= 0.2 X 0.3
= 0.06 (C is the correct answer)
Question 2

Using a zscore
= (890 – 945)/29
= 1.8966
= — 1.9
= 0.0287

Getting two zscores
= (960 – 945)/29
= 0.52
And
= (900 – 945)/29
= 1.55
Subtracting the 2 zscores we get the needed probability
For 0.52 = 0.6985
And for 1.55 = 0.0606
The probability = 0.6985 – 0.0606
= 0.6379

5%, mean of 945 meters squared, standard deviation of 29 square meters
Probability = 0.05
= (5/100 x 945)/29
= 1.63
From ztable
= 0.9484
= 948 square meters
Question 3

Binomial distribution
This is a binomial distribution because there are only 2 outcomes (the order is process online or not)
Let X = number of orders processed online
Here, n= 20, and x = 18. Let p= 0.95(processed online), q = 0.05 (not processed online)
The probability that 18 orders will be processed online:
P(X) = 0.95 x 18/20
= 0.855

2/20 x 5/100
= 0.1 x 0.05
= 0.005

185/200 x 0.95
= 0.879
Question 4

Total number of patrons
= 308 male + 292 female
= 600
Total number of patrons who order dessert
= 90 male + 46 Female
= 136
Probability that a patron orders dessert
= 136/600
= 17/75

Probability of a female patron ordering dessert
= 46/600
= 23/300
17/75 x 23/300
= 182/600
= 91/300

17/75

The events are independent
This is because if a male patron orders a dessert, it does not exclude a female patron from ordering the dessert
Question 5

Rate of bankruptcy 5.5 per week
For 5 businesses to go bankrupt
P(A>5)
= (1/5.5) x 5
= 0.9

20 businesses in 4 weeks
Going bankrupt
P (A=20)
= (1/5.5) x 20/4
= 0.91