normal and binomial distributions
95% of data on the curve lies between
2 standard deviations below the mean and 2 above the mean
normal distribution shape
Bell shaped curve
standard deviation of a binomial
square root of np(1-p)
the area between 1 standard deviation below the mean and 1 above the mean makes up what %
68%
Where is the 10th percentile of the Z distribution? a. -1.28 b. 0.10 c. 1.28 d. 0.90
a. -1.28
X is a normally distributed random variable with mean 50 and standard deviation 5. What is the probability that X will be less than 55? a. 0.023 b. 0.841 c. 0.977 d. 0.159
b. 0.841
Suppose X = exam score and X has a normal distribution with mean 80 and standard deviation 5. Bob scored at the 90th percentile. What is Bob's Z-value (aka Z-score)? a. 86.4 b. 1.28 c. 2 d. 10%
b. 1.28
If an observation has a z-score of -1.5, how many standard deviations is it above or below the mean? a. 0.066 standard deviations above the mean b. 1.5 standard deviations below the mean c. 0.066 standard deviations below the mean d. 1.5 standard deviations above the mean
b. 1.5 standard deviations below the mean
The time (X) to complete a standardized exam is approximately normal with a mean of 70 minutes and standard deviation of 10 minutes. How much time should be given to complete the exam so that 80% of the students will complete the exam in the time given? a. 84.7 minutes b. 78.4 minutes c. 74.8 minutes d. 92.3 minutes
b. 78.4 minutes
When you use the normal distribution to find a probability for a binomial random variable, which of the following is true? a. You needed np and np(-p) to be less than 10. b. You needed np and n(1-p) to be at least 10 and you get an approximate answer. c. None of the other choices is correct d. You are making a mistake.
b. You needed np and n(1-p) to be at least 10 and you get an approximate answer.
If X is a binomial random variable with n = 4 and p = 0.18. What is P(X = 3)? a. 0.981 b. 0.18 c. 0.019 d. 0.75
c. 0.019
The national proportion of adults who are concerned about nutrition is 0.4. You take a random sample of 10 adults and count the number who are concerned about nutrition (call it X). What is the probability that X is less than 2? a. 0.6 b. None of the other choices is correct c. 0.0463 d. 0.9537
c. 0.0463
Suppose 20% of Ohio residents support the legalization of marijuana. If you randomly select n people and would like to use the normal approximation to answer questions, what does your sample size have to be, at minimum? a. 20 b. 10 c. 50 d. 80
c. 50
Suppose X has a normal distribution with mean 80 and standard deviation 5. What is the 90th percentile of X? a. 73.6 b. .90 c. 86.4 d. 90
c. 86.4
Suppose X = number of women in a sample of size 100 from a population that has 80% women and 20% men. X has an approximate normal distribution with mean _____ and standard deviation ______. a. None of the other choices is correct b. 50, 5 c. 80, 16 d. 80, 4
d. 80, 4
If X is binomial with n = 5 and p = 0.05, the chance that X is at least 1 is 0.7738 True False
false
center of a normal distribution
mean
f X is a binomial random variable with n = 15 and p = 0.3, we can use the normal approximation? no yes
no
mean of x for a binomial distribution
np
the kth ___________ is the value of x where k% lies below x
percentile
The 80th percentile of the standard normal (Z) distribution is .84. True False
true
what type of variable is a normal distribution?
continuous
What is the probability that a normally distributed random variable X is greater than 85 if μX= 75 and σX= 4? CHOOSE THE CLOSEST ANSWER. a. 2.5 b. 1 c. 0.994 d. 0.006
d. 0.006
Suppose X has a normal distribution with mean 80 and standard deviation 5. How many standard deviations above or below the mean is 70? a. None of the other choices is correct b. 10 standard deviations below the mean c. 2 standard deviations above the mean d. 2 standard deviations below the mean
d. 2 standard deviations below the mean
Suppose 40% of college students plan to vote in the election. Now suppose we randomly select 200 college students and ask them if they plan to vote. What is the probability that more than 75 of the 200 students sampled plan to vote? a. 24.6% b. 40% c. 37.5% d. 76.4%
d. 76.4%
Which of the following variables has a binomial distribution? a. Neither of these choices has a binomial distribution. b. Both of these choices have binomial distributions. c. Flipping a coin until you get 10 heads and counting the number of flips needed. d. Flipping a coin 10 times and counting the number of heads.
d. Flipping a coin 10 times and counting the number of heads.
what kind of variable is a binomial distribution?
discrete: 1,2,3...,10,..., n: number of times an event happens out of n trials
Which of the following is NOT a condition of the binomial distribution? a. same probability of yes on each trial (p) b. two possible outcomes on each trial (yes/no) c. independent trials d. fixed number of trials (n) e. all of these choices are conditions of the binomial
e. all of these choices are conditions of the binomial
(t/f) The time to complete a standardized exam is approximately normal with a mean of 70 minutes and a standard deviation of 10 minutes. The percentage of the students which take longer than 80 minutes to complete the exam is 84.13%.
false
variance of x for a binomial distribution
np(1-p)
if x has binomial distribution with large enough n, x can be approximately modeled by a normal (z) distribution... what are the conditions?
np>=10 n(1-p)>=10