Minneapolis Community and Technical College

MATH 1150uestion 1
(05.01 LC)
Samuel, a quality assurance inspector at a donut factory, checks for product quality using a random
sample of 7 donuts from a batch of 38, with 14 cake donuts and 24 glazed donuts. Let p̂ be the
proportion of cake donuts in the sample.
Part A: Is the 10% condition met in this case? Justify your answer. (5 points)
Part B: Is the Normal condition met in this case? Justify your answer. (5 points)
A: The 10 percent condition states that the population is greater than 10 times the sample, or 10n. In
other words, the sample size must be no more than 10 percent of the population. In this problem, the
sample size is 7, and the population is 38. This means that 38>10n, or 38>10 times 7, or 70. 38 is not
greater than 70, therefor the 10 percent condition is not met in this case
B: In this problem, p, or the population proportion is 14/38. The conditions of normality are that n times
p and n times 1-p are both greater than 5. n=38 and p, as stated, equals 14/38. This means that n
times p equals 14, and n times 1 minus p equals 24, which are both greater than 5. This means that
both of the normality condition have been met.
Instructor comment: Part B is incorrect.
10/10
Question 2
(05.02 LC)
Given a population mean of 27.1 with a standard deviation of 8.4 and a sample size of 10, answer
these questions:
Part A: What is the standard deviation of the sampling distribution of x̄? Show your work. (5 points)
Part B: What does the sample size need to be if you want the standard deviation of the sampling
distribution of x̄ to be 2.8? Show your work. (5 points)
A: answer--> 2.66 --> SD=8.4 , n=10 --> s=sd/square root n=8.4/squre root of 10=2.66
B: this is n when s =2.8
--> s= SD/square root n --> 2.8=8.4/square root n --> 2.8 square root n=8.4 --> square root n =8.4/2.8
--> square root n =3 --> (square root n)^2=3^2 --> n=9
10/10
Question 3
(05.02 MC)
The amount people pay for cell phone service varies quite a bit, but the mean monthly fee is $55 and
the standard deviation is $22. The distribution is not Normal. Many people pay about $30 for plans with
2GB data access and about $60 for 5GB of data access, but some pay much more for unlimited data
access. A sample survey is designed to ask a simpl