Definitions/Formulas
For a standard normal curve, μ = ___ and σ = ___.
μ = 0, σ = 1
If given x, μ, and σ, how do we calculate z?
z = (x - μ)/σ
Given μ = 493 and σ = 111, find P(x < 600).
The amounts of time employees at a large corporation work each day are normally distributed, with a mean of 7.6 hours and a standard deviation of 0.35 hour. Random samples of size 12 are drawn from the population and the mean of each sample is determined. What is the standard deviation of the sample?
0.1010
If n = 50 and p = .65, find μ and σ
μ = 32.5, σ = 3.3727
For a sample distribution, μx = ___ and σx = ___.
μ, σ/sqrt(n)
Find z when x = 49, μ = 58, and σ = 9
z = -1
Given μ = 12 and σ = 0.2, find P(x > 11.9).
P(x > 11,9) = 0.6915
If μ = 64.3, σ = 2.6, and n = 60, find P(x > 66)
Write the normal probability P(150 < x < 200) as a binomial probability.
P(150.5 < x < 199.5)
When using a normal curve to approximate a binomial distribution, what conditions must be met?
np ≥ 5
nq ≥ 5
Find z when x = 110.37, μ = 96, and σ =21
z = 0.6838
Given μ = 0.425 and σ = 0.005, find P(0.40 < x < 0.42).
P(0.40 < x < 0.42) = 0.1587
The population mean annual salary for environmental compliance specialists is about $63,500. A random sample of 35 specialists is drawn from this population. What is the probability that the mean salary of the sample is less than $60,000? Assume σ = $6100
P(x < 60000) = 0.2831
Sixty-two percent of adults in the United States have an HDTV in their home. You randomly select 45 adults in the United States and ask them if they have an HDTV in their home. Find the mean and standard deviation.
μ = 27.9, σ = 3.2561
Q3 = ___
0.75 or 75%
Find z when p = 0.42
z = -0.2019
Given μ = 0.5 and σ = 0.008, find x when P = 0.16
x = 0.4920
The mean critical reading SAT score is 501, with a standard deviation of 112. A particular high school claims that its students have unusually high critical reading SAT scores. A random sample of 50 students from this school was selected, and the mean critical reading SAT score was 515. Find the probability of a school having a mean score of 515 or higher and determine if the high school is justified in its claim.
P(x ≥ 515) = 0.1884; The school is not justified in its claim.
Five percent of adults in the United States are planning to purchase a 3D TV in the next two years. You randomly select 95 adults in the United States and ask them if they are planning to purchase a 3D TV in the next two years. Can we use a normal distribution to approximate this binomial distribution?
No, np = 4.75
D2 = ___
0.20 or 20%
Find z for D8
z = 0.8416
Given that the average SAT score is 493 and the standard deviation is 111, if 1000 SAT writing scores are randomly selected, about how many would you expect to be greater than 650?
79 scores
A machine in a manufacturing plant is calibrated to produce a bolt that has a mean diameter of 4 inches and a standard deviation of 0.25 inch. An engineer takes a random sample of 25 bolts from this machine and finds the mean diameter is 4.2 inches. What conclusions can the engineer make from his findings?
No conclusions can be made, as n < 30
A drug manufacturer claims that a drug cures a rare skin disease 75% of the time. The claim is checked by testing the drug on 100 patients. If at least 70 patients are cured, this claim will be accepted. Find the probability that the claim will be rejected assuming that the manufacturer’s claim is true.
1 - P(x > 69.5) = 0.1020