1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Lyrx [107]
3 years ago
6

Student records suggest that the population of students spends an average of 6.30 hours per week playing organized sports. The p

opulation's standard deviation is 2.10 hours per week. Based on a sample of 49 students, Healthy Lifestyles Incorporated (HLI) would like to apply the central limit theorem to make various estimates.
A) What is the chance HLI will find a sample mean between 5.5 and 7.1 hours?
B) Calculate the probability that the sample mean will be between 5.9 and 6.7 hours.
Mathematics
1 answer:
Ymorist [56]3 years ago
5 0

Answer:

a) 99.24% chance HLI will find a sample mean between 5.5 and 7.1 hours.

b) 81.64% probability that the sample mean will be between 5.9 and 6.7 hours.

Step-by-step explanation:

To solve this question, it is important to know the Normal probability distribution and the Central Limit Theorem

Normal probability distribution

Problems of normally distributed samples can be 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 = \frac{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 random variable X, with mean \mu and standard deviation \sigma, a large sample size can be approximated to a normal distribution with mean \mu and standard deviation \frac{\sigma}{\sqrt{n}}.

In this problem, we have that:

\mu = 6.3, \sigma = 2.1, n = 49, s = \frac{2.1}{\sqrt{49}} = 0.3

A) What is the chance HLI will find a sample mean between 5.5 and 7.1 hours?

This is the pvalue of Z when X = 7.1 subtracted by the pvalue of Z when X = 5.5.

By the Central Limit Theorem, the formula for Z is:

Z = \frac{X - \mu}{s}

X = 7.1

Z = \frac{7.1 - 6.3}{0.3}

Z = 2.67

Z = 2.67 has a pvalue of 0.9962

X = 5.5

Z = \frac{5.5 - 6.3}{0.3}

Z = -2.67

Z = -2.67 has a pvalue of 0.0038

So there is a 0.9962 - 0.0038 = 0.9924 = 99.24% chance HLI will find a sample mean between 5.5 and 7.1 hours.

B) Calculate the probability that the sample mean will be between 5.9 and 6.7 hours.

This is the pvalue of Z when X = 6.7 subtracted by the pvalue of Z when X = 5.9

X = 6.7

Z = \frac{6.7 - 6.3}{0.3}

Z = 1.33

Z = 1.33 has a pvalue of 0.9082

X = 5.9

Z = \frac{5.9 - 6.3}{0.3}

Z = -1.33

Z = -1.33 has a pvalue of 0.0918.

So there is a 0.9082 - 0.0918 = 0.8164 = 81.64% probability that the sample mean will be between 5.9 and 6.7 hours.

You might be interested in
Four rulers and three pencils cost £2.15
Lubov Fominskaja [6]

Answer:

4r + 3p = 2.15

3r + 4p = 2.05

I have no idea.......

4 0
3 years ago
Grandma is making her grandson french toast. The pan can only fit two pieces of bread at a time. To cook each side of the bread
Anni [7]

Grandma should be able to make three slices of French toast by slicing one of the original slices into two.

<h3>How can grandma make three slices of French toast?</h3>
  • Put two slices of bread in the pan and cook them for one minute (first minute)
  • Turn both slices over and cook ( second minute)
  • Remove both slices and slice one of this into two. This will mean the new slices will have one side cooked and another one that is not cooked.
  • Cook these thinner slices  (third minute).
  • The result would be three cooked slices, although two of them would be thinner.

Learn more about French toast in: brainly.com/question/11713135

#SPJ1

4 0
1 year ago
Write a slope-intercept equation for a line passing through the point (5,-5) that is parallel to the line x = -2. Then write a s
Gnesinka [82]

Answer:

1. y=-2x+5

2. y=1/2x-7.5

Step-by-step explanation:

you plug in the cordinates for the y intercept and you already have the slope.

y=mx+b

m= slope which is -2

6 0
3 years ago
What is the slope of the line that passes through (2,12) and (4,20)
iris [78.8K]

Answer:

D. 4

Step-by-step explanation:

Use rise over run, (y2 - y1) / (x2 - x1)

Plug in the points:

(y2 - y1) / (x2 - x1)

(20 - 12) / (4 - 2)

8 / 2

= 4

So, the slope is 4.

6 0
3 years ago
How many solutions does the following equation have?
Marysya12 [62]

Answer:

b) no solution

Step-by-step explanation:

What you always want to do in this type of problem is to combine all of your "like terms," where like terms are the part of your equation that have the same variable (or no variable). In this equation, we see three terms that have the variable "z". We can add the 12z + 15z on the left side to get 27z, and then we subtract 27z on both sides to cancel both of the 27z terms out.

Now, we are left with -6 = -5   (because we got rid of all the terms with the variable z in them). We know that -6 does not equal -5, and therefore, there is no number that we can assign to variable z such that the left side of the equation will equal the right side of the equation.

Therefore, there is no solution (because a solution to the equation would be a value that we can plug into the variable z to make the equation true).

3 0
3 years ago
Read 2 more answers
Other questions:
  • Students in middle school and high school were surveyed about whether they have taken the SAT. Some of the survey results are li
    6·1 answer
  • Show step by step for equation -8/3x + 4(x + 9/4) = -2/3(x + 12/8) + 3
    15·1 answer
  • What is m<br> Enter your answer in the box.
    14·1 answer
  • Maggie's brother is 6 years younger than four times her age. The sum of their ages is 69.
    9·2 answers
  • A pair of pants costs twice as much as a shirt. The total cost of 1 pair of pants and 1 shirt is $18. If s represents the cost o
    6·2 answers
  • Please if you don’t wanna help you just want points just scroll from me I really need help rn... I’m aboutta burst in tears that
    12·2 answers
  • someone please help me with this if one person already answers then dont answer i only have a few points left and need it for sc
    8·1 answer
  • Which number is greater?<br> 2.2 or 15/4 (it is a fraction)
    5·2 answers
  • 2x=12+12<br><br>x????????????​
    11·2 answers
  • Each of two computers can process bills at 160/min a newer model can process bills at 200/min after the first two computers have
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!