Question

1.

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

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

c.) Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (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 the specified mean and standard deviation. Find the indicated probability. (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 the specified mean and standard deviation. Find the indicated probability. (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 curve lies to the left of z. (Round your answer to two decimal places.) z =

g.) Find z such that 57% of the standard normal curve lies to the right of z. (Round your answer to two decimal places.) z =

h.) 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 = 86 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.)

(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 at 125)

i.) Thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village are approximately normally distributed, with a mean of 4.6 millimeters (mm) and a standard deviation of 1.5 mm. For a randomly found shard, find the following probabilities. (Round your answers to four decimal places.)

(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

Answer 1

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