Download Lecture Note Question:

Lecture Note Question:
The Question about Bakery:
Mean = Xbar = 24
Std Dev = S = 4
1. If a random sample of size n = 1 (day) is selected, what is the probability this x value will
exceed 28?
Here N = 1
P(X>28)
Zscore = (X – Xbar) / S
Zscore = (28 – 24) / 4 = 1
P(X>28) = 0.5 – 0.3413 = 0.1587
2. If a random sample of size n = 4 (days) is selected, what is the probability that Xbar >28?
Here n = 4
P(X>28)
V(Xbar) = 16/ n-1
V(Xbar) = 16/4-1
V(Xbar) = 5.33
S = Sqrt (5.33) = 2.309
Zscore = (X – Xbar) / S
Zscore = (28 – 24) / 2.309 = 1.739 or 2
P(X>28) = 0.5 – 0.4772 = 0.0228
3. Why does the answer in part 1 differ from that in part 2?
The first one uses standard deviation which is equal to the standard deviation of the
population and the value is 4. In the second one the square root of sample variance is
used. Both these populations have normal distributions.