Suppose a research firm conducted a survey to determine the average amount of money steady smokers spend on cigarettes during a week. A sample of 100 steady smokers revealed that the sample mean is $80 and the sample standard deviation is $20. What is the probability that a sample of 100 steady smokers spend between $76 and $84?
A) 0.4772
B) 0.0228
C) 0.9544
D) 0.3400
E) 0.9999

Question

Quizplus · Accepted Answer

Since we know the sample mean and standard deviation, we can use the Central Limit Theorem to approximate the distribution of sample means as a normal distribution with a mean of $80 and a standard deviation of $2 (since sample size is 100). So we want to find the probability that a random variable with a normal distribution with mean $80 and standard deviation $2 falls between $76 and $84. This is the same as finding the area under the standard normal curve between z-scores of -2 and 2 (where z = (x-mean)/standard deviation). Using a standard normal table or calculator, we find this probability to be approximately 0.9544. Therefore, the best choice is C.

Suppose a Research Firm Conducted a Survey to Determine the Average