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
Dvinal [7]
3 years ago
6

Suppose the horses in a large stable have a mean weight of 975lbs, and a standard deviation of 52lbs. What is the probability th

at the mean weight of the sample of horses would differ from the population mean by less than 15lbs if 31 horses are sampled at random from the stable? Round your answer to four decimal places.
Mathematics
1 answer:
Lubov Fominskaja [6]3 years ago
7 0

Answer:

0.8926 = 89.26% probability that the mean weight of the sample of horses would differ from the population mean by less than 15lbs if 31 horses are sampled at random from the stable

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 = \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 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.

In this problem, we have that:

\mu = 975, \sigma = 52, n = 31, s = \frac{52}{\sqrt{31}} = 9.34

What is the probability that the mean weight of the sample of horses would differ from the population mean by less than 15lbs if 31 horses are sampled at random from the stable?

pvalue of Z when X = 975 + 15 = 990 subtracted by the pvalue of Z when X = 975 - 15 = 960. So

X = 990

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

By the Central Limit Theorem

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

Z = \frac{990 - 975}{9.34}

Z = 1.61

Z = 1.61 has a pvalue of 0.9463

X = 960

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

Z = \frac{960 - 975}{9.34}

Z = -1.61

Z = -1.61 has a pvalue of 0.0537

0.9463 - 0.0537 = 0.8926

0.8926 = 89.26% probability that the mean weight of the sample of horses would differ from the population mean by less than 15lbs if 31 horses are sampled at random from the stable

You might be interested in
Given:
nirvana33 [79]
I hope this helps you

5 0
2 years ago
PLS ANSWER THIS IM IN A HURRY
den301095 [7]

Answer:

14.14 i hope this helps lol ;)

6 0
3 years ago
Read 2 more answers
Which statement can be used to prove WX Perpendicular to XY​
sveta [45]

Answer: as long as w x and x y have opposite reciprocals for their slopes they are perpendicular

Step-by-step explanation:

3 0
3 years ago
Please help! I will give brainliest and 5 stars!
Ierofanga [76]

Answer:

(A.) x = y - 4

Step-by-step explanation:

All you need to do is subtract the 4 from both sides, giving you the final equation as x = y - 4.

7 0
3 years ago
In July, 3/5 of the 160 babies born in an area hospital were girls. Seventy of the babies weighed 8 pounds or more. Fifty boys w
mars1129 [50]

Imma guess the middle one

5 0
3 years ago
Read 2 more answers
Other questions:
  • Which equation represents the graph of the linear function?
    5·1 answer
  • What is the percent of 0.6 repeating
    13·2 answers
  • Which of the following best describes the graph of the polynomial function
    11·2 answers
  • Please help me out i need it with these questions!!!!
    10·1 answer
  • If the transformation was a rotation, tiffany can or cannot be certain the trapezoids are congruent?
    8·1 answer
  • Solve x+14=16<br> What is x?
    10·2 answers
  • Insert 16 rational numbers between 2.1 and 2.2​
    13·1 answer
  • What is -6x multiplied by y
    6·2 answers
  • Type the integer that makes the following subtraction sentence true:<br> _____ − –99 = 3
    12·2 answers
  • A triangle with side lengths of 5 meters, 7 meters and 9 meters.
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!