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1. Let z be a random variable with a standard normal distribution. Find the indicated probability....

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Statistics

1. Let z be a random variable with a standard normaldistribution. Find the indicated probability. (Round your answer tofour decimal places.)

P(−2.13 ≤ z ≤ −0.35) =

2. Assume that x has a normal distribution with thespecified mean and standard deviation. Find the indicatedprobability. (Round your answer to four decimal places.)

μ = 14.6; σ = 3.9

P(10 ≤ x ≤ 26) =

3. A person's blood glucose level and diabetes are closelyrelated. Let x be a random variable measured in milligramsof glucose per deciliter (1/10 of a liter) of blood. Suppose thatafter a 12-hour fast, the random variable x will have adistribution that is approximately normal with mean μ = 82and standard deviation σ = 30. Note: After 50years of age, both the mean and standard deviation tend toincrease. For an adult (under 50) after a 12-hour fast, find thefollowing probabilities. (Round your answers to four decimalplaces.)

(a) x is more than 60


(b) x is less than 110


(c) x is between 60 and 110


(d) x is greater than 125 (borderline diabetes starts at125)

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