Question

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

Answer #1

Solution :

a.

P(x < 17) = P[(x - ) / < (17 - 20) / 9]

= P(z < -0.3333)

= 0.3695

Probability = **0.3695**

b.

P(13 < x < 26) = P[(13 - 20)/ 9) < (x - ) / < (26 - 20) / 9) ]

= P(-0.7778 < z < 0.6667)

= P(z < 0.6667) - P(z < -0.7778)

= 0.7475 - 0.2183

= 0.5292

Probability = **0.5292**

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

(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

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.

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

Let "Z" be a random variable from the standard normal
distribution. Find the value for ? that satisfies each of
the following probabilities.
(Round all answers to two decimal places)
A) P(Z < ?) = 0.6829.
? =
B) P(Z > ?) = 0.3087.
? =
C) P(-? < Z < ?) =
0.7402.
? = ±

2.)Assume random variable Z follows standard normal
distribution; find the value of the following probabilities.
P(-1<Z<1)
3.)Assume random variable Z follows standard normal
distribution; find the value of the following probabilities.
P(0<Z<1)
4.)Assume random variable Z follows standard normal
distribution; find the value of the following probabilities.
P(Z>2)
5.)The natural log of growth of yucca tree is approximately
normally distributed with mean of 0.053 mm and standard deviation
0.03mm. Determine the probability that a yucca tree has growth less
than...

Let the random variable X follow a normal distribution with
muμequals=4040 and sigmaσ2equals=6464. a. Find the probability that
X is greater than 5050. b. Find the probability that X is greater
than 2020 and less than 5252. c. Find the probability that X is
less than 4545. d. The probability is 0.30.3 that X is greater than
what number? e. The probability is 0.070.07 that X is in the
symmetric interval about the mean between which two numbers?

Suppose that the random sample is taken from a normal
distribution N(8,9), and the random sample is between 1 to 25.
Find the distribution of the sample mean.
Find probability that the sample mean is less than or equal to
8.8 and the sample variance is less than or equal to 12.45, where
the probabilities are independent.
Find probability that the sample mean is less than 8+(.5829)S,
where S is the sample standard deviation.

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) =

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