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 Precision Writing Instruments Company makes two pen designs - the Cordova design and the Savannah design. These data apply, regardless of which of two pen designs is being implemented. Materials cost per pen is $6. Labor cost per pen is $5. Production overhead is
$1,000,000. Advertising and promotion is $1,000,000. Marketing research has estimated the following demand functions for the next year of sales for the two pen designs where Q represents demand in thousands and P represents price. For the Cordova design, Q = 150 - 2.5P. For the Savannah design, Q = 175 - 2.1P. A penetration strategy is proposed for the Savannah design and a price of $25 is selected. What will be the profit or loss for the first year?

n/33 = 4/11

Please select the best answer from the choices provided

A: n = 90 3/4
B: n = 16
C: n = 1 1/3
D: n = 12​

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 =
Reset
Next

6/8 and 24/40 are they proportional

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

111.2 please help 20 points!!!!

HELPPPPPP I DONT GET THIS AT ALL

Your payment is $375 per month for 36 months and you made a $2,500

What is the solution to the equation 9(x + 2) = 27? (1 point) Group of answer choices x = 2.5 x = 0.5 x = −0.5 x = −3.5

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

Please help me with this problem​

Simplify the expression and choose the appropriate result.
3(2 + 3g)

Which system of equations has no solution?

A.
y = 7x +5
y = 7x + 5

B.
3x - 5y = 10
-3x + 5y = -10

C.
y = 3x - 2
y = 3x + 5

D.
3x - 5y = 10
-3x - 2y = 20

please help me I'm going to fail if you don't help me​

the force of gravity depends on the distance between objects? true or false​

please help with this

Solve forX
9(x + 1) = 25 + x
Ox=2
Ox=3
Ox=4
Ox=5

0.4,0.7,1.0,1.3 what is the sequence rule

Based on a​ survey, assume that ​31% of consumers are comfortable having drones deliver their purchases. Suppose that we want to find the probability that when consumers are randomly​ selected, exactly of them are comfortable with delivery by drones. Identify the values of​ n, x,​ p, and q.

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

Can someone help me I appreciate it

solve the following equation for y

x+y=3​

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.

8xn=24x7 what is the missing number?

Two fair dice, one yellow and one blue, are rolled. The value of the blue die is subtracted from the value of the yellow die. Which of the following best describes the theoretical probability distribution?

dijkstra's algorithm

Logs5(3x-2) = 1 + Logs5 (x-4)

If ∧ ASC ≅ ∧ KSC then ∠8 is congruent to which angle?

A jar contains 24 blue marbles 16 red marbles and 14 white marbles find the simplified ratio of total marbles to red marbles

It says that I need to find x for the missing angle in the equation.