Suppose that the US plans to send a shipment of "rovers" to Mars. These are mobile robots, programmed to collect rock and soil samples, and then return to the landing site. The rovers operate independently of each other. The mean weight a rover is programmed to collect is 50 pounds, and the standard deviation of weights is 5 pounds. Weights collected by rovers are approximately normally distributed. If the US sends 10 rovers, what is the probability that the average weight of rock and soil brought back by these rovers will be between 48 pounds and 52 pounds? What sampling distribution should we use to compute this probability?

Answers

Answer 1

Answer:

Answer:

79.24% probability that the average weight of rock and soil brought back by these rovers will be between 48 pounds and 52 pounds

We use the sampling distribution of the sample means of size 10 to solve this question, by the Central Limit Theorem. They are normally distributed with mean 50 and standard deviation 1.58.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = (X - \mu)/(\sigma)$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = (\sigma)/(√(n))$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

$\mu = 50, \sigma = 5, n = 10, s = (5)/(√(10)) = 1.58$

What is the probability that the average weight of rock and soil brought back by these rovers will be between 48 pounds and 52 pounds?

This is the pvalue of Z when X = 52 subtracted by the pvalue of Z when X = 48. So

X = 52

$Z = (X - \mu)/(\sigma)$

By the Central Limit Theorem

$Z = (X - \mu)/(s)$

$Z = (52 - 50)/(1.58)$

$Z = 1.26$

$Z = 1.26$ has a pvalue of 0.8962

X = 48

$Z = (X - \mu)/(s)$

$Z = (48 - 50)/(1.58)$

$Z = -1.26$

$Z = -1.26$ has a pvalue of 0.1038

0.8962 - 0.1038 = 0.7924

79.24% probability that the average weight of rock and soil brought back by these rovers will be between 48 pounds and 52 pounds

What sampling distribution should we use to compute this probability?

We use the sampling distribution of the sample means of size 10 to solve this question, by the Central Limit Theorem. They are normally distributed with mean 50 and standard deviation 1.58.

Related Questions

A child has $6.17 in change in her piggy bank. The change consists of 113 coins in a mix of pennies, nickels, and quarters. If there are 8 times as many nickels as pennies, how many of each coin does the child have?
Please I need help I dont know what to do
6. How many solutions does the given system have?y = 3x - 16x - 2y = -2A. one solutionB. two solutionsC. infinite solutionsD. no solution
What is the zero of f?-52-25
Classify the following triangle as acute, obtuse, or right.30°249126

Write the slope-intercept form of the equation : a) 4x-2y = 3

Answers

Answer:

$y = 2x - (3)/(2)$

Step-by-step explanation:

slope-intercept form: y = mx + b

Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. PEMDAS is the order of operations and stands for:

Parenthesis

Exponents (& Roots)

Multiplications

Divisions

Additions

Subtraction

First, subtract 4x from both sides of the equation:

4x (-4x) -2y = (-4x) + 3

-2y = -4x + 3

Next, divide -2 from both sides of the equations:

$((-2y))/(-2) = ((-4x + 3))/(-2)$

$y = (-4)/(-2)x + (3)/(-2)$

$y = 2x - (3)/(2)$

$y = 2x - (3)/(2)$ is your answer.

Linda enrolls for 10 credit hours for each two semsters at a cost of $600 per credit hour. in addition textbooks $400 per semster.

Answers

Answer:

$6800

Step-by-step explanation:

1. Assuming your question was how much is her cost the total cost should amount to $6800.

2. First you should multiply 10 by 600 to find out the cost for the credit hours

3. Next you take the cost of textbooks into factor, with each being 400 a semester you add them together to get $800

4. You add both costs together and get the final price of $6800 for both semesters of her education.

Final answer:

Linda's total cost for college for this academic year is calculated as $12,800, encompassing both tuition and textbooks. This is part of an observed trend in increasing higher education costs.

Explanation:

Cost of Tuition: Linda is paying $600 per credit hour for 20 credit hours (10 each semester), so $600 * 20 = $12,000 in total for tuition.

Cost of Textbooks: She is also spending $400 per semester for textbooks, so $400 * 2 = $800 in total for textbooks.

Total Cost: Thus, Linda's total cost for the academic year would be the sum of these two costs, i.e, $12,000 + $800 = $12,800. The costs of tuition, textbooks and other expenses are part of the rising trend of higher education costs. Despite this, the value of education still remains high, as it can lead to better job prospects and higher earning potential in the future.

Learn more about College Costs here:

brainly.com/question/20629475

#SPJ3

Basic Geometric Shapes Answer the questions below. When you are finished, submit this assignment to your teacher by the due date for full credit. Total score: ____ of 15 points (Score for Question 1: ___ of 3 points) 1. All numbered streets runs parallel to each other. Both 3rd and 4th Streets are intersected by King Ave. as shown: a. Hint: Think about it from the cars perspective. The angle youre finding is the inside angle of the cars turn. (a) Suppose a car is traveling east on 4th Street and turns onto King Avenue heading northeast. What is the measure of the angle created by the car's turning? Explain your answer. (b) Suppose a car is traveling southwest on King Avenue and turns left onto 3rd Street. What is the measure of the angle created by the car's turning? Explain your answer. (c) Suppose a car is traveling northeast on King Avenue and turns right onto 3rd Street. What is the measure of the angle created by the car's turning? Explain your answer.

Answers

Answer:

(a)105° (b)105° (c)105°

Step-by-step explanation:

The Question Image is attached and a labeled one for explanation.

(a)If the Car is travelling east from the direction point A and heads North East on Kings Avenue in the direction of E, the angle which the car makes is Angle AFE

Angle AFE=180-75=105°

(b)If a car is traveling southwest on King Avenue and is to turn left onto 3rd Street. His probable starting point is North of 3rd street, say F. The angle created is Angle FGC.

Angle AFE =Angle FGC (Corresponding Angles)

Angle FGC =105°

(c)Suppose a car is traveling northeast on King Avenue is to turn right onto 3rd Street. His starting point will be South of 3rd Street.

Angle HGD will be the angle with which it turns.

Angle HGD= Angle CGE(Vertically Opposite Angles)

Angle HGD=105°

What is the measure of the angle created by the car's turning? Explain your answer.

Jack buys a bag of 5 apples, eachequal in size. He eats of 1/2 of one apple.
What fraction of the bag of
apples did he eat?

Answers

Answer:

4 1/2

Step-by-step explanation:

5 apples - 1/2 apple =

4 1/2 apple

9/2

How many units long is side w?
A. 14
B. 6.2
C. 22
d. 5.5

Answers

Answer:

d. w is 5.5 units

Step-by-step explanation:

$(11)/(16) = (w)/(8)$

$16w = 88$

$w = 5.5$

So d is correct.

Brian has $88 and he saves $3.50 a week how many more weeks will it take him to get to 200

Answers

Answer:

32 weeks

Step-by-step explanation:

First you should write an equation for this word problem. Since you know Brian wants to save to $200, the equation will equal 200. Then you figure out how much he has already, which is 88. Right now, the equation we have is 88+(weekly savings)= 200. He saves 3.50 a week, so the equation will finally look like 88+3.50x=200. X is how many weeks it will take for him to reach 200. We then move everything so that it all equals X. You would move the 88 first which will then give 3.50x=112. Dividing by 3.50 on both sides would give X as 32. SO the number of weeks it will take for Brian to save to $200 is 32 weeks.

Other Questions

Kendra sold 200 shares through her broker in June 8. The price per share was $22.10. The broker charged her a 0.5% commission on the total value. What was Kendra’s return on the trade?

If apple=5, orange=6 and strawberry=10 then banana=?

Which expression is equivalent to 2la+26)-2-26?

PLEASE HELP ME ASAP!