Binomial and Geometric Distributions Worksheetap Stat
Binomial and Geometric Distributions WorksheetAP Stat
1. Lefties. Assume that 13% of people are left handed. If we select 5 people at random, find the following probabilities.
a)The first lefty is the fifth person.
b)There are some lefties among the 5 people.
c)The first lefty is the second or third person.
d)There are exactly 3 lefties in the group.
e)There are no more than 3 lefties in the group.
f)How many lefties do you expect? With what standard deviation?
g)What is the probability that the majority are left handed?
2. Chips. Suppose a computer chip manufacturer rejects 2% of the chips produced because they fail presale testing.
a) What is the probability that the fifth chip you test is the first bad one you find?
b) What is the probability that you find a bad one within the first ten you examine?
c) What is the expected number of chips you need to check until you find a good chip?
3. Blood. Only 4% of people have type AB blood.
a) On average, how many donors must be checked to find someone with type AB blood?
b) What is the probability that there is a type AB donor among the first 5 people checked?
c) What is the probability that we won’t find a type AB donor before the 10th person?
4. Colorblindness. About 8% of males are colorblind. A researcher needs some colorblind subjects for and experiment and begins checking potential subjects.
a) On average, how many men should the researcher expect to check to find someone who is colorblind? With what standard deviation?
b) What is the probability that she won’t find any anyone colorblind among the first four men she checks?
c) What is the probability that exactly 3 people out of the first 20 checked are colorblind?
d) What is the probability that there are at least 4 people out of the first 50 checked who are colorblind?
e) What is the probability that she finds someone who is colorblind before checking the 10th man?
5. Athletes. Major universities claim that 72% of the senior athletes graduate that year. Fifty senior athletes attending major universities are randomly selected whether or not they graduate is recorded in the order of selection.
a) What is the probability that exactly 40 senior athletes graduated that year?
b) What is the probability that exactly 35 or 36 senior athletes graduated that year?
c) What is the probability that fewerthan 38 senior athletes graduated that year?
d) What is the probability that 40 or more senior athletes graduated that year?
e) What is the probability that the first senior athlete to graduate from the selected group was the 5th selected?
f) What is the probability that the first senior athlete to graduate from the selected group was within the first 8 selected?
g) What is the expected number of senior athletes to graduate that year?
h) What is the standard deviation of senior athletes to graduate that year?
Binomial and Geometric Distributions WorksheetAP Stat
1. Lefties. Assume that 13% of people are left handed. If we select 5 people at random, find the following probabilities.
a)The first lefty is the fifth person.
b)There are some lefties among the 5 people.
c)The first lefty is the second or third person.
d)There are exactly 3 lefties in the group.
e)There are no more than 3 lefties in the group.
f)How many lefties do you expect? With what standard deviation?
g)What is the probability that the majority are left handed?
2. Chips. Suppose a computer chip manufacturer rejects 2% of the chips produced because they fail presale testing.
a) What is the probability that the fifth chip you test is the first bad one you find?
b) What is the probability that you find a bad one within the first ten you examine?
c) What is the expected number of chips you need to check until you find a good chip?
3. Blood. Only 4% of people have type AB blood.
a) On average, how many donors must be checked to find someone with type AB blood?
b) What is the probability that there is a type AB donor among the first 5 people checked?
c) What is the probability that we won’t find a type AB donor before the 10th person?
4. Colorblindness. About 8% of males are colorblind. A researcher needs some colorblind subjects for and experiment and begins checking potential subjects.
a) On average, how many men should the researcher expect to check to find someone who is colorblind? With what standard deviation?
b) What is the probability that she won’t find any anyone colorblind among the first four men she checks?
c) What is the probability that exactly 3 people out of the first 20 checked are colorblind?
d) What is the probability that there are at least 4 people out of the first 50 checked who are colorblind?
e) What is the probability that she finds someone who is colorblind before checking the 10th man?
5. Athletes. Major universities claim that 72% of the senior athletes graduate that year. Fifty senior athletes attending major universities are randomly selected whether or not they graduate is recorded in the order of selection.
a) What is the probability that exactly 40 senior athletes graduated that year?
b) What is the probability that exactly 35 or 36 senior athletes graduated that year?
c) What is the probability that fewer than 38 senior athletes graduated that year?
d) What is the probability that 40 or more senior athletes graduated that year?
e) What is the probability that the first senior athlete to graduate from the selected group was the 5th selected?
f) What is the probability that the first senior athlete to graduate from the selected group was within the first 8 selected?
g) What is the expected number of senior athletes to graduate that year?
h) What is the standard deviation of senior athletes to graduate that year?