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.)

Answer #1

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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 = 52 and standard
deviation σ = 6.4, find the following probabilities. (Round your
answers to four decimal places.) (a) P(x ≤ 60) Incorrect: Your
answer is incorrect. (b) P(x ≥ 50) Incorrect: Your answer is
incorrect. (c) P(50 ≤ x ≤ 60) Incorrect: Your answer is
incorrect.

(1)Given that x is a normal variable with mean μ = 52 and
standard deviation σ = 6.9, find the following probabilities.
(Round your answers to four decimal places.) (a) P(x ≤ 60) (b) P(x
≥ 50) (c) P(50 ≤ x ≤ 60) (2) Find z such that 15% of the area under
the standard normal curve lies to the right of z. (Round your
answer to two decimal places.) (3) The University of Montana ski
team has six entrants...

Suppose X is a normal random variable with mean
μ = 100 and standard deviation σ = 7. Find
b such that
P(100 ≤ X ≤
b) = 0.3.
HINT [See Example 3.] (Round your answer to one decimal
place.)
b =

a.)A normal random variable X has unknown mean μ and standard
deviation σ = 6. What is the margin of error E for a 98 percent
confidence interval for μ, based on a random sample of size
b.)(b) What sample size would be needed in part (a) to have a
margin of error

Using the formulas for the mean and standard deviation of a
discrete random variable, calculate to 2 decimal places the mean
and standard deviation for the population probability distribution
of the table below.
x
P(x)
69
0.20
79
0.22
81
0.35
98
0.23
μ =
σ =

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