Question

7. A normal random variable *x* has mean *μ* = 1.7
and standard deviation *σ* = 0.17. Find the probabilities of
these *X*-values. (Round your answers to four decimal
places.)

(a) 1.00 < * X* <
1.60

(b)

(c) 1.25 < * X* < 1.50

8. Suppose the numbers of a particular type of bacteria in samples of 1 millilitre (mL) of drinking water tend to be approximately normally distributed, with a mean of 81 and a standard deviation of 8. What is the probability that a given 1-mL sample will contain more than 98 bacteria? (Round your answer to four decimal places.)

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A normal random variable x has mean μ = 1.7 and standard
deviation σ = 0.16. Find the probabilities of these X-values.
(Round your answers to four decimal places.)
(a) 1.00 < X < 1.50 =
(b) X > 1.35 =
(c) 1.45 < X < 1.50 =

A normal random variable x has mean μ = 1.6 and standard
deviation σ = 0.19. Find the probabilities of these X-values.
(Round your answers to four decimal places.)
1.00 < X < 1.20
X > 1.37
1.35 < X < 1.50

A normal random variable x has mean ? = 1.7
and standard deviation ? = 0.12. Find the probability
associated with each of the following intervals. (Round your
answers to four decimal places.)
(a)
1.00 < x < 1.40
(b)
x > 1.34
(c)
1.25 < x < 1.50

Given that x is a normal variable with mean μ
= 51 and standard deviation σ = 6.5, find the following
probabilities. (Round your answers to four decimal places.)
(a) P(x ≤ 60)
(b) P(x ≥ 50)
(c) P(50 ≤ x ≤ 60)

Given that x is a normal variable with mean μ
= 48 and standard deviation σ = 6.2, find the following
probabilities. (Round your answers to four decimal places.)
(a) P(x ≤ 60)
(b) P(x ≥ 50)
(c) P(50 ≤ x ≤ 60)

Given that x is a normal variable with mean μ = 111 and standard
deviation σ = 14, find the following probabilities. (Round your
answers to four decimal places.) (a) P(x ≤ 120) (b) P(x ≥ 80) (c)
P(108 ≤ x ≤ 117)

Given that x is a normal variable with mean μ
= 43 and standard deviation σ = 6.5, find the following
probabilities. (Round your answers to four decimal places.)
(a) P(x ≤ 60)
(b) P(x ≥ 50)
(c) P(50 ≤ x ≤ 60)

Given that x is a normal variable with mean μ = 43 and standard
deviation σ = 6.7, find the following probabilities. (Round your
answers to four decimal places.) (a) P(x ≤ 60) (b) P(x ≥ 50) (c)
P(50 ≤ x ≤ 60)

Given that x is a normal variable with mean μ = 42 and standard
deviation σ = 6.1, find the following probabilities. (Round your
answers to four decimal places.) (a) P(x ≤ 60) (b) P(x ≥ 50) (c)
P(50 ≤ x ≤ 60)

Suppose the numbers of a particular type of bacteria in samples
of 1 millilitre (mL) of drinking water tend to be approximately
normally distributed, with a mean of 81 and a standard deviation of
9. What is the probability that a given 1-mL sample will contain
more than 102 bacteria? (Round your answer to four decimal
places.)

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