Question

The size of fish is very important to commercial fishing. Suppose the length of Atlantic cod caught in nets has a mean of 49.5 cm and a standard deviation of 3.71 cm. The length of fish is normally distributed. A sample of 14 fish is taken.

State the random variable.

• The mean length of Atlantic cod caught in nets.
• The standard deviation of lengths of Atlantic cod caught in nets.
• The length of Atlantic cod caught in nets.

Find the mean of the sample mean.
μ_x̄ =

Find the standard deviation of the sample mean. Round to two decimal places.
σ_x̄ =

What is the shape of the sampling distribution of the sample mean? Why?

• The sampling distribution of the sample mean is normally distributed since the population is normally distributed.
• The sampling distribution of the sample mean is unknown since the population of the random variable is not normally distributed and the sample size is less than 30.
• You can say the sampling distribution of the sample mean is not normally distributed since the sample size is less than 30.

Find the probability that the sample mean is less than 48. Round to four decimal places.
P(x̄ < 48) =

Find the probability that the sample mean is less than 61. Round to four decimal places.
P(x̄ > 61)=

If you did find a sample mean of more than 61 would you find that unusual? What could you conclude?

• Since it is unusual for a sample mean to be more than 61, it may indicate that the population mean has changed.
• Since it is not unusual for a sample mean to be more than 61, it may indicate that the population mean has changed.
• Since it is not unusual for a sample mean to be more than 61, there is no evidence that the population mean has changed.
• Since it is unusual for a sample mean to be more than 61, there is no evidence that the population mean has changed.

Answer 1