Question

The average teacher salary in Nebraska is $52,925 with a standard deviation of $12,115. We collect a random sample of 50 Nebraska teachers and record their salary.

Part 1: (6 pts)

Check all necessary conditions in detail (not just yes or no) and give the sampling model and parameters to the nearest dollar.

Part 2: (6 pts)

What is the probability that the average teacher salary in our sample of 50 teachers is less than $50,000? Find the z-score and probability. Be sure you use the appropriate p-value notation! Then write a sentence that summarizes your results.

Answer #1

Part 1.

Note that n=50>30. So, we can use central limit theorem.

Part 2.

The average teacher salary in Nebraska is $52,925 with a
standard deviation of $12,115. We collect a random sample of 50
Nebraska teachers and record their salary.
Part 1: (6 pts) Check all necessary conditions in detail (not
just yes or no) and give the sampling model and parameters to the
nearest dollar.
Part 2: (6 pts) What is the probability that the average teacher
salary in our sample of 50 teachers is less than $50,000? Find the
z-score and...

In Colorado, the average ACT score is 20.1 with a standard
deviation of 1.3. We collect a random sample of 35 students who
took the exam last year.
Part 1: (6 pts) Check the all necessary conditions in detail
(not just yes or no) (1 pt each) and give the sampling model and
parameters to 2 decimal places (2 pts).
Part 2: (8 pts) What is the probability that the average
composite ACT score is 19.5 or less? Show your...

In Colorado, the average ACT score is 20.1 with a standard
deviation of 1.3. We collect a random sample of 35 students who
took the exam last year.
Part 1: (6 pts)
Check the all necessary conditions in detail (not just yes or
no) (1 pt each) and give the sampling model and parameters to 2
decimal places (2 pts).
Part 2: (8 pts)
What is the probability that the average composite ACT score is
19.5 or less? Show your...

The average teacher’s salary is $45,000. Assume a normal
distribution with standard deviation equal to $10,000. a) What is
the probability that a randomly selected teacher makes greater than
$65,000 a year? b) If we sample 100 teachers’ salaries, what is the
probability that the sample mean will be greater than $65,000?

[5] 3. The
average teacher’s salary is $45,000. Assume a normal distribution
with standard
deviation equal to $10,000.
What is the probability that a randomly selected teacher makes
greater than $65,000 a year?
If we sample 100 teachers’ salaries, what is the probability
that the sample mean will be greater than $65,000?

To estimate a student’s average score, we need to
collect a sample. Assume population standard deviation is equal to
3, If we want to control the error within 0.2 with 98% confidence
level, how large the sample size need to be?

The average score for games played in the NFL is 21.5 and the
standard deviation is 9.3 points. 46 games are randomly selected.
Round all answers to 4 decimal places where possible and assume a
normal distribution.
What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
What is the distribution of ∑x∑x? ∑x∑x ~ N(,)
P(¯xx¯ > 20.9432) =
Find the 74th percentile for the mean score for this sample
size.
P(21.9432 < ¯xx¯ < 23.3856) =
Q1 for the...

1. Customers at the local Subway store order an ice tea with
their meal 70% of the time. Use the Binomial distribution to find
the answer to the following.
Find the probability that among the next 8 customers, at least 3
will order ice tea with their meal: (to three places
after the decimal)
Of the next 8 customers, how many do you expect to order ice tea
with their meal? (to one place after the decimal)
2. The average score of...

A random sample is selected from a population with mean μ = 100
and standard deviation σ = 10.
Determine the mean and standard deviation of the x sampling
distribution for each of the following sample sizes. (Round the
answers to three decimal places.)
(a) n = 8 μ = σ =
(b) n = 14 μ = σ =
(c) n = 34 μ = σ =
(d) n = 55 μ = σ =
(f) n = 110...

HW9-Practice: Problem 3
Problem Value: 1 point(s). Problem
Score: 50%. Attempts Remaining:
Unlimited.
(1 point) Fueleconomy.gov, the official US government source for
fuel economy information, allows users to share gas mileage
information on their vehicles. The histogram below shows the
distribution of gas mileage in miles per gallon (MPG) from 14 users
who drive a 2012 Toyota Prius. The sample mean is 53.3 MPG and the
standard deviation is 5.2 MPG. Note that these data are user
estimates and since...

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