Question

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

Answer #1

Solution: We know that for standard normal variable X, mean is 0 and variance is 1.

i.e

Now, we have to calculate P(Z>1.53)

Using standard normal table, we get

Therefore,

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)

Z is a standard normal random variable. Compute the following
probabilities.
a.
P(-1.33 Z 1.67)
b.
P(1.23 Z 1.55)
c.
P(Z 2.32)
d.
P(Z -2.08)
e.
P(Z -1.08)

Find the following probabilities for the standard normal random
variable z. (Round your answers to four decimal places.)
(a) P(−1.43 < z < 0.64) =
(b) P(0.52 < z < 1.75) =
(c) P(−1.56 < z < −0.48) =
(d) P(z > 1.39) =
(e) P(z < −4.34) =

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...

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)

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.

For the standard normal random variable, z, find the
following:
P(z > 2.45) =
P(z > -5.33) =
P(-1.33 < z < 2.45) =
P(1.33 < z < 2.45) =
Please be as detailed as possible, thank
you.

Given that z is a standard normal random variable, compute the
following probabilities (to 4 decimals). P(-1.98 ≤ z ≤ 0.48) P(0.55
≤ z ≤ 1.29) P(-1.73 ≤ z ≤ -1.08)

Given that Z is a standard normal random variable, compute the
following probabilities (to 4 decimal places).
a. P(-1.98 ≤ z ≤ 0.49)
b. P(.55 ≤ z ≤ 1.28)
c. P(-1.79 ≤ z ≤ -1.09)

Find these probabilities for a standard normal random variable
Z. Be sure to draw a picture to check your calculations. Use the
normal table or software.
(a)
P(Zless than<1.11.1)
(d)
P(StartAbsoluteValue Upper Z EndAbsoluteValueZgreater
than>0.40.4)
(b)
P(Zgreater than>negative 1.4−1.4)
(e)
P(negative 1.4−1.4less than or equals≤Zless than or
equals≤1.11.1)
(c)
P(StartAbsoluteValue Upper Z EndAbsoluteValueZless
than<1.61.6)

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