stats hw

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1

know
n	1000		Z = 1.645
s	5.9
m	245
Construct a 90% CI
		lower number		upper number
		subract margin of error		add your margin of error

A sample of 1000 items has a population standard deviation of 5.9 and a mean of 245. Construct a 90 percent confidence interval for μ.

2

Know
n	250	LN	UN
mean	33.65
Sta dev	1.85
z	1.96

At the end of 2016, 2017, and 2018, the average prices of a share of stock in a portfolio were $34.75, $34.65, and $31.25 respectively. To investigate the average share price at the end of 2020, a random sample of 250 stocks was drawn and their closing prices on the last trading day of 2020 were observed with a mean of 33.65 and a standard deviation of 1.85. Estimate the average price of a share of stock in the portfolio at the end of 2020 with a 95 percent confidence interval.

3

know
u
sta dev
n
z
	LN	UN

A research study investigated differences between male and female students. Based on the study results, we can assume the population mean and standard deviation for the GPA of male students are µ = 3.25 and σ = 0.57. Suppose a random sample of 5000 male students is selected and the GPA for each student is calculated. Find the interval that contains 99 percent of the sample means for male students.

4

Know

mean

sta dev

P (X > 33)

0.561

???

0.439

mean=32.5

sta dev=3.25

0.439

A manufacturing company measures the weight of boxes before shipping them to the customers. If the box weights have a population mean of 32.5 lb and standard deviation of 3.25 lb, respectively, then based on a sample size of 500 boxes, what is the probability that the average weight of the boxes will exceed 33 lb?

5

			mean of a binomial distribution =				n * p = u
			variance of a binomial distribution = n p ( 1 - p ) =

If n = 52 and p = 0.66, then the standard deviation of the binomial distribution is

6

P ( X > 6 customers arriving within a minute)
	0.8558
	u = 4.3	6

Consider a Poisson distribution with an average of 4.3 customers per minute at the local grocery store. If X = the number of arrivals per minute, find the probability of more than 6 customers arriving within a minute.

7

An important part of the customer service responsibilities of a cable company is the speed with which trouble in service can be repaired. Historically, the data show that the likelihood is 0.75 that troubles in a residential service can be repaired on the same day. For the first 6 troubles reported on a given day, what is the probability that all 6will be repaired on the same day?

8

z score		In the text	5-4
	knowns
	mean
	std dev
	n
	P ( X > 2.85)

An apple juice producer buys all his apples from a conglomerate of apple growers in one northwestern state. The amount of juice obtained from each of these apples is approximately normally distributed with a mean of 2.75 ounces and a standard deviation of 0.11 ounce. What is the probability that a randomly selected apple will contain more than 2.85 ounces?

9

z score
Z = (X-u) / Sta Dev		Solve for x
Knowns
mean	45
Sta Dev	7

Suppose that the waiting time for a license plate renewal at a local office of a state motor vehicle department has been found to be normally distributed with a mean of 45 minutes and a standard deviation of 7 minutes. Suppose that in an effort to provide better service to the public, the director of the local office is permitted to provide discounts to those individuals whose waiting time exceeds a predetermined time. The director decides that 10 percent of the customers should receive this discount. What number of minutes do they need to wait to receive the discount?

10

	z score for sampling distribution
	?
	P ( x bar > 88)			z = ( x bar - u ) / sta dev / sq root of n
				= (88-88.5) / 5.75
				-0.0869565217
				=standardize * SQRT(n)

A random sample of size 350 is taken from a population with mean 88.5 and standard deviation 5.75. Find P(x bar > 88).