1. The mean annual US household income is $72,641. Suppose that the standard deviation is $30,000. a. Find the probability that a household chosen at random has an income greater than $100,000. b. Find the probability that a group of 5 households, chosen at random, have an average income greater than $100,000. c. Find the probability that a group of 10 households, chosen at random, have an average income greater than $100,000.

Answer:

The answer is below

Step-by-step explanation:

The z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given as:

[tex]z=\frac{x-\mu}{\sigma}\\\\where\ x=raw\ score,\mu=mean\ and\ \sigma=standard\ deviation \\\\For\ a\ sample\ size\ n: \\\\z=\frac{x-\mu}{\sigma/\sqrt{n} }[/tex]

Given that μ = $72,641 and σ = $30,000.

a) x > $100000

[tex]z=\frac{100000-72641}{30000}=0.91[/tex]

P(x > 100000) = P(z > 0.91) = 1 - 0.8186 = 0.1814

b) n = 5

x > $100000

[tex]z=\frac{100000-72641}{30000/\sqrt{5} }=2.04[/tex]

P(x > 100000) = P(z > 2.04) = 1 - 0.9793 = 0.0207

c) n = 10

x > $100000

[tex]z=\frac{100000-72641}{30000/\sqrt{10} }=2.88[/tex]

P(x > 100000) = P(z > 2.88) = 1 - 0.9980 = 0.002

The sum of two consecutive integers is 199. Find the integers

A shoe company wants to test an updated model of a running shoe on its wear after one month of running. They recruit 50 people who run on a regular basis to participate in the study. They will have the runners wear the shoes when they run for two months. After two months, the wear on the shoes will be determined using the depth of the tread and flexibility of the toe box. The wear between the new model and the original model will then be compared. The company decides to use a matched pairs design and devises two options.

Option A: The 50 subjects are paired based on running ability. The fastest two runners are paired together, the next fastest two, etc. For each pair of runners, the researcher will flip a coin. If the coin lands on heads, then the first runner will receive the new model of shoes and the second runner will receive the original model. If the coin lands on tails, the first runner will receive the original model of shoes and the second runner will receive the new model. After 2 months of use, the difference in wear for the pairs of runners will be determined.

Option B: The 50 subjects will each receive both models of shoes. At the beginning, the runner will flip a coin, and if it lands on heads, they will wear the new model on their right foot and the original model on their left foot. Then after one month, they will change and use the new model on their left foot and the original model on their right foot. After the second month, the wear for each model will be determined and compared for the 50 runners.

Which option should the shoe company use to compare the two models?

A: The runners are paired based on their running ability. This will provide an accurate comparison for the difference in wear between the original model and the new model.
B: Each runner varies with respect to multiple variables. Each runner should use both models to account for their individual differences. This will provide an accurate comparison for the difference in wear between the models.
Both A and B: Both provide an accurate comparison for the difference in wear between the original model and the new model. The runners are paired in option A based on running ability, and each runner uses both models in option B.
Neither A nor B: Neither provides an accurate comparison to determine the difference in wear for the two models. This experiment should be a randomized block design.

Can someone help me I appreciate it

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The sample space is a collection of outcomes from an event?

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12
Type the correct answer in the box. Use numerals instead of words.
What is the solution to this equation?
7-32 - x = 12
The solution is I =
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Next

Part C
Question
Determine the missing values in the table.
Recall that x represents the number of tickets sold and y represents the amount of money earned from ticket sales.
Type the correct answer in each box. Use numerals instead of words.
X
$20
3
6
20
$400

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