A random sample of size n is to be drawn from a population with mu = 700 and sig

Question

A random sample of size n is to be drawn from a population with mu = 700 and sigma = 200. What size sample would be necessary in order to reduce the standard error to 10? n = 400 The daily revenue at Sparty has been recorded for the past five years. Records indicate that the mean daily revenue is $1500 and the standard deviation is $500. The distribution is skewed to the right due to several high volume days (football game days). Suppose that 100 days are randomly selected and the average daily revenue computed. Which of the following describes the sampling distribution of the sample mean? A) skewed to the right with a mean of $1500 and a standard deviation of $500 B) normally distributed with a mean of $150 and a standard deviation of $50 C) normally distributed with a mean of $1500 and a standard deviation of $500 D) normally distributed with a mean of $1500 and a standard deviation of $50 One year, the distribution of salaries for professional sports players had mean $1.6 million and standard deviation $0.7 million. Suppose a sample of 100 major league players was taken. Find the approximate probability that the average salary of the 100 players that year exceeded $1.1 million. A .2357 B) approximately 0 C) .7357 D) approximately 1

Explanation / Answer

a. standard error=sd/sqrt(n), now se=10 and sd=200

So sqrt(n)=sd/se=200/10=20

Hence n=400

b. As per central limit theorem for n sufficient large sampling mean will have normal distribution with mean=mu and se=sd/sqrt(n)

So mean=mu=1500 and sd=500/10=50 so d is answer.

c. sampling mean will be distributed with mean=1.6 and sd=0.7/10=0.07

Hence P(xbar>1.1)=P(z>1.1-1.6/0.07)=P(z>-7.1)=1 so answer is d

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