Math 1P98 - Practical Statistics PDF

PRACTICAL STATISTICS
STUDENT ID:
[Pick the date]

Question 1
a) The requisite z value is 0.8750.
b) The area 0.1908 can be interpreted as the probability of the length of human pregnancy
exceeding 280 days.
c) The z value for top 10% is 1.28
Hence, the minimum pregnancy time = Z*standard deviation + Mean = 1.28*16 + 266 =
286.48 days
d) The z value for bottom 5% is -1.645
Hence, the maximum pregnancy time = Z*standard deviation + Mean = -1.645*16 + 266 =
239.68 days
Question 2
It is known that μ = 138.5 seconds and σ = 29 seconds
a) We use the following formula
Z = (X-μ)/ σ
Here X= 100
Z = (100-138.5)/29 = -1.3276
P(Z<-1.3276) = 0.092
b) We use the following formula
Z = (X-μ)/ σ
Here X= 160
Z = (160-138.5)/29 = 0.7414
P(Z>0.7414) = 1- P(Z≤0.7414) = 1- 0.7708 = 0.2292

c) Here X1 = 120 seconds
Z1 = (120-138.5)/29 = -0.6379
P(Z<Z1) = 0.2618
Also, X2 = 180 seconds
Z2 = (180-138.5)/29 = 1.43
P(Z<Z1) = 0.9238
Hence, P (Z1<Z<Z2) = 0.9238-0.2618 = 0.6620
d) Here X = 300 seconds
Z = (180-138.5)/29 = 1.43
P(Z<1.43) = 0.9238
Hence, P(Z>5.569) = 1-0.9238 = 0.0762
Thus, it can be concluded that it would not be unusual for a car to spend in excess of 3
minutes in the drive thru as the underlying probability exceeds 0.05.
Question 3
a) Population mean (μ) = (151+122+120+131)/4 = 131 minutes
b) The possible samples with 2 samples are as follows.
1) (151,122)
2) (151,120)
3) (151, 131)
4) (122, 120)