If a random variable X has the normal distribution with mean u80.0 and standard deviation o 4.8, i) Find the probability that it will take on a value between 71.6 and 88.4, that is P (71.6 xo) 0.025 1 ii)

A college alumni Organization sent a survey to all recent graduates to ask their annual income. 20% of the alumni responded, and their mean annual income was $40,000  with a standard deviation of $10,000. Explain why these data should not be used to construct a confidence interval for the mean annual income of all recent graduates.

A population of values has a normal distribution with μ=139.8μ=139.8 and σ=54.4σ=54.4. You intend to draw a random sample of size n=87n=87.a.) Find the probability that a single randomly selected value is greater than 121.1.P(X > 121.1) = b.) Find the probability that a sample of size n=87n=87 is randomly selected with a mean greater than 121.1.P(M > 121.1) =  (Here M is the mean of the sample)Enter your answers as numbers accurate to 4 decimal places.

Assume the random variable X is normally distributed with a mean of 130 and standard deviation of 21.5. State answers to THREE decimals.   P (140 < x < 165) = P( x > 105) =

A person's blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean μ = 88 and standard deviation σ = 21. Note: After 50 years of age, both the mean and standard deviation tend to increase. For an adult (under 50) after a 12-hour fast, find the following probabilities. (Round your answers to four decimal places.) (a) x is more than 60(b) x is less than 110(c) x is between 60 and 110(d) x is greater than 140 (borderline diabetes starts at 140)