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
denis-greek [22]
3 years ago
14

A distribution of values is normal with a mean of 60 and a standard deviation of 16. From this distribution, you are drawing sam

ples of size 25. Find the interval containing the middle-most 76% of sample means.
Mathematics
1 answer:
professor190 [17]3 years ago
3 0

Answer:

The interval containing the middle-most 76% of sample means is between 56.24 and 63.76.

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 normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes 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 = \frac{\sigma}{\sqrt{n}}.

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

A distribution of values is normal with a mean of 60 and a standard deviation of 16.

This means that \mu = 60, \sigma = 16

Samples of size 25:

This means that n = 25, s = \frac{16}{\sqrt{25}} = 3.2

Find the interval containing the middle-most 76% of sample means.

Between the 50 - (76/2) = 12th percentile and the 50 + (76/2) = 88th percentile.

12th percentile:

X when Z has a p-value of 0.12, so X when Z = -1.175.

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

By the Central Limit Theorem

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

-1.175 = \frac{X - 60}{3.2}

X - 60 = -1.175*3.2

X = 56.24

88th percentile:

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

1.175 = \frac{X - 60}{3.2}

X - 60 = 1.175*3.2

X = 63.76

The interval containing the middle-most 76% of sample means is between 56.24 and 63.76.

You might be interested in
What is the measure ??
alexandr402 [8]
Welcome

d the answer is 73 degrees
114 - 41 = 73
5 0
3 years ago
A dance school has 63 ballet dancers. If 42% of the total number of dancers in the school are ballet dancers, what is the total
maria [59]
The total number of dancers in the school is 150.
7 0
3 years ago
Write an equation of a line that is perpendicular to the given line and that passes through the given point.
devlian [24]
Here is the answer I believe. It goes in a x all it did was added to to each x and y (-3,0)
8 0
3 years ago
Help me do this i will pick brailest if right and it is 45 points!
sweet-ann [11.9K]

Answer:

8/21

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Nonpermissable replacement for a 4/9a?
My name is Ann [436]
If a=0, then the denominator is equal to 0.  Since you cannot divide by zero, you are not allowed to do this.
Hope This helps!

8 0
3 years ago
Other questions:
  • Mr. Design is covering rectangular pieces of plywood with fabric to create a wall hanging. Each piece has an area if 12 3/4 squa
    13·2 answers
  • An average person’s hair grows at a rate of 18 cm per year. How fast in inches per month does the average person’s hair grow? Sh
    9·2 answers
  • A TUB USES 20 GALLONS. a shower uses 15 gallons. if 40 people take a bath instead of a shower, how much extra water is used?
    5·2 answers
  • Catherine walks her dog 3/4 mile everyday. how far does she walk each day?
    6·2 answers
  • What is x+y=-20 and 6x-5y=-20 with elimination method
    10·1 answer
  • In a triangle the second angle measures twice the first and the third angle measures 5 more than the second. If the sum of the a
    5·1 answer
  • How do you break apart 3 x 5
    10·1 answer
  • A recipe calls for 5 1/2 cups of flour. Lorenzo only has 3 1/4 cups of flour. Write and solve an equation to find the additional
    5·1 answer
  • What is the total cost of the menu? The total cost of the menu is $______ (approximately 2 decimal places)
    10·1 answer
  • Help please i know its alot but i am in danger of failing for the year if i fail this test :(
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!