1.
The empirical rule says that 95% of the population is within 2
standard deviations of the mean, but when I find the z-scores that
mark off the middle 95% of the standard normal distribution I
calculate -1.96 and 1.96. Is this a contradiction? Why or why not?
In other words why are the normal distribution calculators not
agreeing with the empirical rule? [2 sentences]
2.
Answer the following:
What is a sampling distribution?
[2 sentences]
What is the Central...
3. A) Given that z is a standard normal random variable, compute
the probability that it takes on a value between -2 and -1.
3. B). Given that z is a standard normal random variable, find
the z-score for a situation where the area to the right of z is
0.0901.
Find the value of the probability of the standard normal random
variable Z corresponding to this area. (Round your answer to four
decimal places.) P(−1.68 < Z < 1.23) =?
Calculate the probability For the standard normal distribution
random variable Z using Excel
formulae/functions.
P (Z ≤ 2)
P (-1.63 < Z ≤ 1.95)
P (-1 < Z < 1)
P (Z ≤ -0.69)
P (0.85 < Z ≤ 2.23)
P (Z > 3)
Find the probability that the Normal random variable with mean
20 and standard deviation 3.2 will generate an outlier (outside the
inner fences) observation. Remember that the lower (upper) inner
fence is 1.5*IQR below (above) the first (third) quartile.
a.
0.0035
b.
0.0051
c.
0.0058
d.
0.0062
e.
0.0070
a) Let z be a random variable with a standard normal
distribution. Find the indicated probability. (Round your answer to
four decimal places.)
P(−2.02 ≤ z ≤ −0.31) =
Shade the corresponding area under the standard normal
curve.
b) Assume that x has a normal distribution with the
specified mean and standard deviation. Find the indicated
probability. (Round your answer to four decimal places.)
μ = 50; σ = 15
P(40 ≤ x ≤ 47) =
c) Find z such...
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 ≤ 1.23) =
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 ≥ −1.13) =
C: Let z be a random variable with a standard normal
distribution. Find the indicated probability. (Round your answer to
four decimal places.)
P(−1.87 ≤ z...