Question

Find the following probabilities based on the standard normal
variable *Z*.

1. a.P(−0.9 ≤ Z ≤ −0.59)b.P(0.04 ≤ Z ≤ 1.72)c.P(−1.4 ≤ Z ≤ 0.06)d.P(Z > 3.6)

Answer #1

We have to use software or Standard Normal table to find its value, I will use R studio here.

R code: pnorm(z)

1)

2)

3)

4)

R Code and output:

> pnorm(-0.59) [1] 0.2775953 > pnorm(-0.9) [1] 0.1840601 > pnorm(1.72) [1] 0.9572838 > pnorm(0.04) [1] 0.5159534 > pnorm(0.06)-pnorm(-1.4) [1] 0.4431655 > pnorm(3.6) [1] 0.9998409

Find the following probabilities based on the standard normal
variable Z.
a.P(Z > 1.12) ____
b.P(Z ≤ −2.35) _____
c.P(0 ≤ Z ≤ 1.34) ______
d.P(−0.8 ≤ Z ≤ 2.44) ______

Find the following probabilities based on the standard normal
variable Z. (You may find it useful to reference
the z table. Leave no cells blank
- be certain to enter "0" wherever required. Round your answers to
4 decimal places.)
a.
P(−1.01 ≤ Z ≤ −0.71)
b.
P(0.01 ≤ Z ≤ 2.45)
c.
P(−1.38 ≤ Z ≤ 0.06)
d.
P(Z > 3.2)

*I'm having trouble with d.
Find the following probabilities based on the standard normal
variable Z. (You may find it useful to reference
the z table. Leave no cells blank
- be certain to enter "0" wherever required. Round your answers to
4 decimal places.)
a. P(-0.9 ≤ Z ≤ -0.44)
b. P(0.03 ≤ Z ≤1.5)
c. P(1.46 ≤ Z ≤ 0.05)
d. P(Z > 4)

Let X represent a binomial random variable with n = 170 and p =
0.6. Find the following probabilities. (Do not round intermediate
calculations. Round your final answers to 4 decimal places.)
Probability
a.P(X ≤ 100)
b.P(X > 110)
c.P(105 ≤ X ≤ 115)
d.P(X = 90)

Find the following probabilities based on the standard normal
variable Z. (Use Excel to get the
probabilities. Round your answers to 4 decimal
places.)
a.
P(Z > 1.12)
b.
P(Z ≤ −2.35)
c.
P(0 ≤ Z ≤ 1.34)
d.
P(−0.8 ≤ Z ≤ 2.44)

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

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...

Find the probabilities associated with the standard normal
random variable Z:
a) P (Z> 2.54)
b) P (-3.2 <Z <3.2)
c) P (Z <1.94)
d) P (Z> 2.88)
e) P (Z> 3.15)

Find the following probabilities for the standard normal random
variable z. (Round your answers to four decimal
places.)
(a) P(?1.41 < z < 0.61) =
(b) P(0.55 < z < 1.78) =
(c) P(?1.54 < z < ?0.44) =
(d) P(z > 1.32) =
(e) P(z < ?4.31) =
You may need to use the appropriate appendix table or technology to
answer this question.

Given that Z is a standard normal random variable, compute the
following probabilities. Draw a curve and shade appropriate region.
Use TI-83 calculator to find the probabilities
(i) P( z ≤ 1.0)
(ii) P( z ³ 1.0)
(iii) P( z ≤ -1.0)
(iv) P(-1.0 ≤ z ≤ 1.0)
(v) P(-1.6 ≤ z ≤ 1.2)

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