Mod 4
You are required to read 7 books from a list of 12. How many different orders can you do so?
Permutation; 3,991,680 ways
What is the formula to find a z-score?
z = (x - mean)/population standard deviation
Can we use the Central Limit Theorem to a sample size of 20?
No, CLT can only be used in sample sized of 30 or greater
An interval estimate associated with a certain level of confidence is…
A confidence interval
What do H0 and Ha stand for?
H0 = Null hypothesis
Ha = Alternative hypothesis
You have 9 movies, and you are bringing 5 on vacation with you. How many ways can you pack them if order doesn’t matter?
Combination; 126 ways
Find the z score of 52 if it is located on a normal distribution graph with a mean of 46 and a standard deviation of 5.
z = 1.2
What is the equation for the standard deviation of a sampling distribution?
Population standard deviation/ the square root of n
How do you find the value of the level of significance?
1 - level of confidence
Write the null and alternative hypothesis: A liquor company claims that the liquor they produce is good after opening for an average of at most 10 months. specify the claim.
H0 = mean (less than or equal to) 10 ©
Ha = mean > 10
Solve this binomial: A bag contains 15 tortilla chips from Border Grill. 6 chips are yellow, 2 chips are red and the rest are blue. 3 chips are selected with replacement. Find the probability that you select exactly one blue chip.
0.396069
Find the area under a standard normal curve given the following z scores:
Z < 1.65
Z > -0.31
-0.65 < z < 1.52
Z < 1.65 = 0.95053
Z > -0.31 = 0.6217
-0.65 < z < 1.52 = 0.6779
A population of unknown distribution has a mean of 13.7 and a standard deviation 3.5. If a sample of size 69 is taken. Find the probability that 12 < x < 18.
0.5768
Find the sample size: You need to be 95% confident that you are within $500 of the mean price required to buy a yacht in your city. What is the minimum sample size required? Assume population standard deviation is known to be $1600.
n = 40
What is a type 1 error?
When the null is true, but we reject it
Solve this Geometric distribution: the casino says that 1 every 100 pulls win a slots game. You decide to pull a lever on the slots until you win. Determine the probability that the first time you win is in:
The 1st pull,
The 45th pull
and the 89th pull
The 1st pull = 0.01
The 45th pull = 0.00643
The 89th pull = 0.00413
Find the z score of each area:
Area to the left z = 0.6527
Area to the right z = 0.4768
Area between -z and z = 0.2951
Area to the left z = 0.6527: z = 0.39
Area to the right z = 0.4768: z = 0.06
Area between -z and z = 0.2951: z = -0.38, 0.38
A population of an unknown distribution has a mean 16.7 and a standard deviation 4.8. If the sample size 57 are taken about 79% of the sample means will be less than what value?
17.21
In a study of 756 musicians, 48% responded that they started off playing piano. Find a 90% confidence interval for the population proportion of all musicians who started off playing piano.
E = 0.0300
(0.45, 0.51)
Of the following tests (Left, right, two tailed?), what kind of test are we doing if
H0: mean (less than or equal to) k
Ha mean > k
Right tailed test
Solve this Poisson distribution: suppose Anna drinks 15.2 coffees per month and that this number follows a Poisson distribution. Find the probability that:
She drinks 20 coffees in a randomly selected month
0.0446
A population has a mean of 9.3 and a standard deviation of 1.2. Find the value of P24. (The 24th percentile)
8.45
A population of an unknown distribution has a mean 21.6 and a standard deviation of 2.1. If a sample of a size 50 is taken, find the probability that 750 < SumX < 1100.
0.9110
In a survey of 145 Bay College students, 52 responded that they get tutored in at least one subject. Find the point estimate for a 95% confidence interval for the population proportion of all Bay College students.
(0.28056, 0.43668)
McDonald's in Escanaba has received several complaints that that they are receiving only 9 chicken nuggets in their 10-piece nugget meal. McDonald’s randomly selects 15 customer’s orders and finds the sample mean to be 9.8 nuggets in each meal. The population standard deviation is 0.2 nuggets. What does the evidence suggest at a 4% level of significance?
H0: mean (greater than or equal to) 10
Ha: mean < 10 (cl)
N = 15
Population Standard Deviation = 0.2
Alpha (fish) = 0.04
X bar = 9.8
Z = -3.87
P = 0.000054
P < alpha
Therefore, we reject the H0; There is enough evidence to support the claim