3. A random variable is normally distributed. It has a mean of 266 and a standard deviation of 26.

If you take a sample of size 11, can you say what the shape of the sampling distribution for the sample mean is? Why?

a) If the sample size is 11, then you can say the sampling distribution of the sample mean is not normally distributed since the sample size is less than 30.

b) If the sample size is 11, then you can say the sampling distribution of the sample mean is normally distributed since the variable is normally distributed.

c) If the sample size is 11, then you can't say anything about the sampling distribution of the sample mean, since the population of the random variable is not normally distributed and the sample size is less than 30.

For a sample of size 11, state the mean of the sample mean and the standard deviation of the sample mean. Round to two decimal places if necessary. _x = _______ _x = _________

For a sample of size 11, find the probability that the sample mean is more than 259. P(x > 259) = ________

If you take a sample of size 36, can you say what the shape of the distribution of the sample mean is? Why?

a) If the sample size is 36, then you can't say anything about the sampling distribution of the sample mean, since the population of the random variable is not normally distributed and the sample size is greater than 30.

b) If the sample size is 36, then you can say the sampling distribution of the sample mean is not normally distributed since the sample size is greater than 30.

c) If the sample size is 36, then you can say the sampling distribution of the sample mean is normally distributed since the variable is normally distributed.

For a sample of size 36, state the mean of the sample mean and the standard deviation of the sample mean. Round to two decimal places if necessary. _x = ______ _x = _______

For a sample of size 36, find the probability that the sample mean is more than 259.P(x > 259) = ________

4: The systolic blood pressure of adults in the USA is nearly normally distributed with a mean of 122 millimeters of mercury (mmHg) and standard deviation of 16.

Someone qualifies as having Stage 2 high blood pressure if their systolic blood pressure is 160 or higher.Stage 1 high BP is specified as systolic BP between 140 and 160.

Give your answers rounded to 4 decimal places. a. What is the probability that an adult in the USA has stage 2 high blood pressure?_________ b. What is the probability that an adult in the USA has stage 1 high blood pressure?______________ c. Your doctor tells you you are in the 30th percentile for blood pressure among US adults. What is your systolic BP? _______ mmHg

d. What is the systolic blood pressure that cuts off the top 2.5% of adults in the USA?_______________ mmHg