Question

(Please describe each solution step in detail.)

Given a random variable having the normal distribution with µ=16.2 and σ 2 = 1.5625, find the probabilities that it will take on a value:

a) greater than 16.8;

b) less than 14.9;

c) between 13.6 and 18.8;

d) between 16.5 and 16.7

Answer #1

To calculate the required probability we will use standard normal variate.

Given a random variable having the normal distribution with mean
? = 7 and ?2 = 49, find the probabilities that it will
take on a value:
a) greater than 6
b) less than 2
c) between 6 and 18.8

A random variable having a normal distribution with ? = 20 ???
?? = 9 find the probabilities that it will:
a. Take on a value less than 17
b. Between 13 and 26

Let the random variable X follow a normal distribution with µ =
19 and σ2 = 8. Find the probability that X is greater than 11 and
less than 15.

Let the random variable X follow a normal distribution with µ =
18 and σ2 = 11. Find the probability that X is greater than 10 and
less than 17.

Let z denote a random variable having a normal distribution with
μ = 0 and σ = 1. Determine each of the probabilities below. (Round
all answers to four decimal places.) (a) P(z < 0.1) = (b) P(z
< -0.1) = (c) P(0.40 < z < 0.84) = (d) P(-0.84 < z <
-0.40) = (e) P(-0.40 < z < 0.84) = (f) P(z > -1.25) = (g)
P(z < -1.51 or z > 2.50) =

Let z denote a random variable having a normal
distribution with μ = 0 and σ = 1. Determine each
of the probabilities below. (Round all answers to four decimal
places.)
(a) P(z < 0.1) =
(b) P(z < -0.1) =
(c) P(0.40 < z < 0.85) =
(d) P(-0.85 < z < -0.40)
=
(e) P(-0.40 < z < 0.85) =
(f) P(z > -1.26) =
(g) P(z < -1.49 or z > 2.50) =

If X is a normal random variable that has a mean of µ = 20 and a
standard deviation σ = 2, (a) the standardized value of X=16 is
_________. (b) What is the probability that X is less than or equal
to 16? __________ (c) What is the probability that X is greater
than 16? __________ (d) What is the probability that X is equal to
16?________

Let the random variable X follow a normal distribution with µ =
18 and σ = 4. The probability is 0.99 that X is in the symmetric
interval about the mean between two numbers, L and U (L is the
smaller of the two numbers and U is the larger of the two numbers).
Calculate L.

Let the random variable X follow a normal distribution
with µ = 22 and σ = 4. The probability is 0.90
that Xis in the symmetric interval about the mean between
two numbers, L and U (L is the smaller of the two numbers and U is
the larger of the two numbers). Calculate U.

1) let X be a continuous random
variable that has a normal distribution with a mean of 40 and a
standard deviation of 5. Find the probability that X
assumes a value:
a. between 32 and
35 b. between 41 and 50
c. greater than
43 d. less than 49

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