Question

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 0.053 mm in a year?

6.)The natural log of growth of yucca tree is approximately normally distributed with mean of 0.053 mm and standard deviation 0.03mm. Calculate the Z score associate with the growth 0.083

7.)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 more than 0.083mm in a year

8.)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 0.023 mm in a year

Answer #1

For a random variable Z, that follows a standard normal
distribution, find the values of z required for these probability
values
P(Z<z)=.5
P(Z<z)=.1587
P(Z<z)=.8413

-. For what follows, Z denotes the standard normal random
variable.
(1) P(Z<1.26) is about
(a) 0.7924
(b) 0.3962
(c) 0.1038
(d) 0.6038
(e) 0.8962
(2) P(-0.54 < Z < 0.78) is about
(a) 0.2054
(b) 0.0769
(c) 0.4877
(d) 0.2823
(e) 0.6877
-Assume the random variable X is normally distributed with mean
172 and standard deviation 10. Find the following
probabilities.
(3) P(X<160)
(a) 0.8849
(b) 0.1151
(c) 0.9999
(d) 0.8078
(e) 0.8438
(4) P(X>150)
(a) 0.0139
(b) 0.9861...

A: Let z be a random variable with a standard normal
distribution. Find the indicated probability. (Round your answer to
four decimal places.)
P(z ≤ 1.11) =
B: Let z be a random variable with a standard normal
distribution. Find the indicated probability. (Round your answer to
four decimal places.)
P(z ≥ −1.24) =
C: Let z be a random variable with a standard normal
distribution. Find the indicated probability. (Round your answer to
four decimal places.)
P(−1.78 ≤ z...

Find the following probabilities for a standard normal random
variable z : p(z > 1.53) with steps

1. If Z is a standard normal random variable, find the
value z0 for the following probabilities. (Round your
answers to two decimal places.)
(a) P(Z > z0) = 0.5
z0 =
(b) P(Z < z0) = 0.8686
z0 =
(c) P(−z0 < Z < z0) = 0.90
z0 =
(d) P(−z0 < Z < z0) = 0.99
z0 =
2. A company that manufactures and bottles apple juice uses a
machine that automatically fills 64-ounce bottles. There is some...

A. For a standard normal distribution, find:
P(-1.14 < z < -0.41)
B. For a standard normal distribution, given:
P(z < c) = 0.0278
Find c.
C. For a standard normal distribution, find:
P(z > c) = 0.4907
Find c.
D. Assume that z-scores are normally distributed with a mean
of 0 and a standard deviation of 1.
IfP(0<z<a)=0.4686P(0<z<a) = 0.4686
find a.
E. Assume that the readings at freezing on a bundle of
thermometers are normally distributed with a...

a) Assume Z is a random variable with a standard normal
distribution and d is a positive number. If P(Z>d)=0.15 then P(
-d<Z<d)=0.7.
True or False
b) If Z is a random variable from a standard normal distribution
and if P(Z>c)=0.27,then P(Z< -c)= 0.27
True or False
c) If Z is a random variable from a standard normal distribution
and if P(Z <b)=0.66, then P(Z,< - b)=0.34
True or False
d) If X represents a random variable coming from a...

A continuous random
variable Z follows standard normal distribution.
a) What is the mean of
Z?
b) What is the
standard deviation of Z?
c) Z=(x-10)/5 What is
the distribution of X ?

1. For a standard normal distribution,
find:
P(z > 2.32)
Keep four decimal places.
2. For a standard normal distribution,
find:
P(-0.9 < z < 0.95)
3. For a standard normal distribution,
given:
P(z < c) = 0.7622
Find c.
4. For a standard normal distribution,
find:
P(z > c) = 0.1753
Find c
5. Assume
that the readings at freezing on a batch of thermometers
are normally distributed with a mean of 0°C and a standard
deviation of 1.00°C....

2. Let the random variable Z follow a standard normal
distribution, and let z1 be a possible value of Z that is
representing the 10th percentile of the standard normal
distribution. Find the value of z1. Show your
calculation.
A. 1.28
B. -1.28
C. 0.255
D. -0.255
3. Given that X is a normally distributed random variable with a
mean of 52 and a standard deviation of 2, the probability that X is
between 48 and 56 is: Show your...

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