Question

In: Statistics and Probability

The amount of hay (measured in pounds) that an adult horse can eat in a day...

The amount of hay (measured in pounds) that an adult horse can eat in a day is uniformly distributed between ten and twenty pounds.

a. What is the average amount of hay that horses eat? What is the standard deviation?

b. What is the probability that a randomly selected horse eats more than fifteen pounds of hay in a day?

c. What is the sampling distribution for the average amount of hay that fifteen horses can eat in a day? Identify the parameters of this distribution and state any theorems used to arrive at this conclusion.

d. What is the probability that the average amount of hay that fifteen horses can eat in a day is more than fifteen pounds?

e. What is the minimum average amount of hay eaten in a day for the top ten percent of all samples of fifteen horses?

Solutions

Expert Solution

Let X is a random variable shows the amount of hay. Here X has uniform distribution between 10 and 20 so pdf of X is

(a)

The average amount of hay that horses eat is

The standard deviation is

(b)

The probability that a randomly selected horse eats more than fifteen pounds of hay in a day is

Answer: 0.50

(c)

Sample size: n=15

Using central limit theorem, the sampling distribution of sample mean will be approximately normal distribution with mean

and standard deviation is

(d)

The z-score for is

The probability that the average amount of hay that fifteen horses can eat in a day is more than fifteen pounds is

Answer: 0.50

(e)

Here we need z-score that has 0.10 area to its right. The z-score 1.28 has 0.10 area to its right.

The minimum average amount of hay eaten in a day for the top ten percent of all samples of fifteen horses will be

Answer: 15.95 pounds


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