A study on the latest fad diet claimed that the amounts of weight lost by all people on this diet had a mean of 20.3 pounds and a standard deviation of 3.7 pounds. Step 1 of 2 : If a sampling distribution is created using samples of the amounts of weight lost by 94 people on this diet, what would be the mean of the sampling distribution of sample means? Round to two decimal places, if necessary.

Step-by-step explanation:

Given that a study A study on the latest fad diet claimed that the amounts of weight lost by all people on this diet had a mean of 20.3 pounds and a standard deviation of 3.7 pounds

Sampling is done for 94 people

According to central limit theorem if random samples are taken for large sizes, the sample mean would follow a normal distribution with mean = population mean.

Hence expected mean value of the sampling distribution = 20.3 ±margin of error

provided samples are drawn at random

Margin of error for 95% = 1.96 (3.7/sqrt 106) = 0.704

Hence mean of sample would lie between

(19.596, 21.004)

= (19.60,21.00)