Question

The number of lightning strikes on a square kilometer of open ground in a year has mean 5.8 and standard deviation 3.5. (These values are typical of much of the United States.) The National Lightning Detection Network uses automatic sensors to watch for lightning in a sample of 40 randomly chosen square kilometers.

(a) What are the mean and standard deviation of X, the mean number of strikes per square kilometer?

μ_X =  (Use 1 decimal place)
σ_X =  (Use 3 decimal places)

(b) What is the probability that X is 5.3 or less? (Use 3 decimal places)

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Sheila's doctor is concerned that she may suffer from gestational diabetes (high blood glucose levels during pregnancy). There is variation both in the actual glucose level and in the blood test that measures the level. A patient is classified as having gestational diabetes if her glucose level is above 150 milligrams per deciliter (mg/dl) one hour after a sugary drink. Sheila's measured glucose level one hour after the sugary drink varies according to the Normal distribution with μ = 135 mg/dl and σ = 14 mg/dl.

Let X = Sheila's measured glucose level one hour after a sugary drink

(a) P(X > 150) =  Use 3 decimal places)

Suppose measurements are made on 3 separate days and the mean result is compared with the criterion 150 mg/dl.

(b) P(X > 150) =  (Use 3 decimal places)

(c) What sample mean blood glucose level is higher than 95% of all other sample mean blood glucose levels? Hint: this requires a backward Normal calculation. (Use 2 decimal places)

Answer 1