1.

a.) Let z be a random variable with a standard normaldistribution. Find the indicated probability. (Enter your answer tofour decimal places.) P(−2.20 ≤ z ≤ 1.01)  =

b.) Let z be a random variable with a standard normaldistribution. Find the indicated probability. (Round your answer tofour decimal places.) P(−1.76 ≤ z ≤ −1.17)  =

c.) Assume that x has a normal distribution with thespecified mean and standard deviation. Find the indicatedprobability. (Round your answer to four decimal places.) μ= 15.1; σ = 4.1

P(10 ≤ x ≤ 26) =

d.) 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 = 3.6

P(8 ≤ x ≤ 12) =

e.) Assume that x has a normal distribution with thespecified mean and standard deviation. Find the indicatedprobability. (Round your answer to four decimal places.) μ= 100; σ = 15

P(x ≥ 120) =

f.) Find z such that 3.0% of the standard normal curvelies to the left of z. (Round your answer to two decimalplaces.) z =

g.) Find z such that 57% of the standard normal curvelies to the right of z. (Round your answer to two decimalplaces.) z =

h.) 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 = 86and standard deviation σ = 21. 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.)

(i) x is more than 60

(ii) x is less than 110

(iii) x is between 60 and 110

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

i.) Thickness measurements of ancient prehistoric NativeAmerican pot shards discovered in a Hopi village are approximatelynormally distributed, with a mean of 4.6 millimeters (mm) and astandard deviation of 1.5 mm. For a randomly found shard, find thefollowing probabilities. (Round your answers to four decimalplaces.)

(i) the thickness is less than 3.0 mm
(ii) the thickness is more than 7.0 mm
(iii) the thickness is between 3.0 mm and 7.0 mm