Can someone please help me with these questions?

1) A government sample survey plans to measure the LDL (bad) cholesterol level of a SRS of men aged 20 to 34. Suppose that in fact the LDL cholesterol level of all men aged 20 to 34 follows the Normal distribution with mean = 115 milligrams per deciliter (mg/dL) and standard deviation = 15 mg/dL. Using the sampling distribution of sample mean, what is the probability that the sample mean takes a value between 114 and 116 mg/dL? This is the probability that the sample mean estimates within 1 mg/dL. (Round your answer to three decimal places.)

• Choose a SRS of 1000 men from this population. This changes the sampling distribution of sample mean. Now what is the probability that the sample mean falls within 1 mg/dL of ? The larger sample is much more likely to give an accurate estimate of . (Round your answer to three decimal places.)

2) The gypsy moth is a serious threat to oak and aspen trees. A state agriculture department places traps throughout the state to detect the moths. Traps are checked periodically, and the distribution of moth counts is discrete and strongly skewed. Most traps have no moths but some traps have several moths. The mean number of moths per trap is only 0.9 with standard deviation 1.3.

• What are the mean and standard deviation of the average number of moths sample mean in 60 traps? (Round your mean to one decimal place and your standard deviation to three decimal places.) mean=? standard deviation=?
• Use the result of the central limit theorem (with the previous parameter values) to find the probability that the average number of moths in 60 traps is greater than 1. (Round your answer to three decimal places.)

3) Consider the following questions about critical values. Find the Normal critical value z* for confidence level C = 80% (Round to two decimal places.) z* =

• How much area is in each tail of the Normal distribution when finding this z* (enter a decimal, not percentage).
• Find the t critical value t* for confidence level C = 85% assuming we take a sample of 50. t* =

4) The National Institute of Standards and Technology (NIST) supplies "standard materials" whose physical properties are supposed to be known. For example, you can buy from NIST an iron rod whose electrical conductivity is supposed to be 10.1 at 293 kelvin. (The units for conductivity are microsiemens per centimeter. Distilled water has conductivity 0.5.) Of course, no measurement is exactly correct. NIST knows the variability of its measurements very well, so it is quite realistic to assume that the population of all measurements of the same rod has the Normal distribution with mean equal to the true conductivity and standard deviation = 0.2. Here are six measurements on the same standard iron rod, which is supposed to have conductivity 10.1.

10.07 9.88 10.03 10.16 10.21 10.11

• NIST wants to give the buyer of this iron rod a 90% confidence interval for its true conductivity. What is this interval? (Round your answers to two decimal places.)

5) We have survey data on the body mass index (BMI) of 656 young women. The mean BMI in the sample was sample mean=26 with sample standard deviation s=6.

Find the margin of error for 95% confidence based on the sample (using a t* value. Round your answers to three decimal places). n = 656 m=?

• Now assume the sample had either 396 young women and 1613 young women instead. n = 396 m =?
• n = 1613 m =?

Thank you!