Use a normal approximation to find the probability of the indicated number of voters. In this case, assume that 170 eligible voters aged 18-24 are randomly selected. Suppose a previous study showed that among eligible voters aged 18-24, 22% of them voted. Probability that fewer than 43 voted.
The probability that fewer than 43 of 170 eligible voters voted is
In: Statistics and Probability
if The number of days with precipitation amounts to 0.01 inches what is the probability of having exactly 10 days of precipitation in the month of April? What is the probability of having less than three days of precipitation in the month of April? What is the probability of having more than 15 days of precipitation in the month of April?
In: Statistics and Probability
A number between 1 and 10 is chosen at random . What is the probability of getting a multiple of 5 or an even number?
In: Statistics and Probability
(In this problem first find the probability by using SPSS and then calculate the number of trees manually by using the probabilities.)
A certain variety of pine tree has a mean trunk diameter of μ=150 cm, and a standard deviation of σ=30 cm which is normally distributed. A certain section of a forest has 500 of these trees.
Find Approximately
1. how many of these trees have a diameter smaller than 120
2. how many of these trees have a diameter greater than 160
3. how many of these trees have a diameter between 130 and 160.
4. how many of these trees have a diameter between 120 and 140.
In: Statistics and Probability
Use a normal approximation to find the probability of the indicated number of voters. In this case, assume that 123 eligible voters aged 18-24 are randomly selected. Suppose a previous study showed that among eligible voters aged 18-24, 22% of them voted.
Probability that exactly 31 voted
The probability that exactly 31 of 123 eligible voters voted is ?
.
In: Statistics and Probability
Use a normal approximation to find the probability of the indicated number of voters. In this case, assume that 144eligible voters aged 18-24 are randomly selected. Suppose a previous study showed that among eligible voters aged 18-24, 22% of them voted.
Probability that fewer than 34 voted
The probability that fewer than 34 of 144 eligible voters voted is?
In: Statistics and Probability
A) A local bakery has determined a probability distribution for the number of cheesecakes that they sell in a given day. Let xx equal the number of cheesecakes sold on a randomly selected day.
| xx | |||||
| 0 | 5 | 10 | 15 | 20 | |
| P(x)P(x) | 0.12 | 0.29 | 0.35 | ? | 0.1 |
What is the probability of selling 15 cheesecakes in a given
day?
P(x=15)=P(x=15)=
What is the probability of selling at least 10 cheesecakes?
P(x≥10)=P(x≥10)=
What is the probability of selling 5 or 15 cheesecakes?
P(x=5P(x=5 or x=15)=x=15)=
What is the probability of selling 25 cheesecakes?
P(x=25)=P(x=25)=
What is the probability of selling at most 10 cheesecakes?
P(x≤10)=P(x≤10)=
Give the expected number of cheesecakes sold on any given day using
the discrete probability distribution?
μ=μ=
B)
Consider the discrete random variable XX given in the table
below. Calculate the mean, variance, and standard deviation of XX.
Also, calculate the expected value of XX. Round solution to three
decimal places, if necessary.
| xx | 6 | 7 | 9 | 20 |
|---|---|---|---|---|
| P(x)P(x) | 0.09 | 0.7 | 0.14 | 0.07 |
μμ =
σ2σ2 =
σσ =
What is the expected value of XX?
E(X)=E(X)=
C)
The probability distribution for the number of students in statistics classes at IRSC is given, but one value is missing. Fill in the missing value, then answer the questions that follow. Round solutions to three decimal places, if necessary.
| xx | P(x)P(x) |
|---|---|
| 26 | 0.1 |
| 27 | 0.14 |
| 28 | 0.17 |
| 29 | |
| 30 | 0.12 |
Find the mean number of students in a Statistics class at
IRSC:
μ=μ=
Find the standard deviation of the number of students in a
Statistics class at IRSC:
σ=σ=
D)
The following table gives the probability distribution of a
discrete random variable XX. Use the table to find the following
probabilities. Round solutions to three decimal places, if
necessary.
| xx | P(x)P(x) |
|---|---|
| 0 | 0.286 |
| 1 | 0.271 |
| 2 | 0.157 |
| 3 | 0.129 |
| 4 | 0.086 |
| 5 | 0.071 |
P(x=2)=P(x=2)=
P(x≤4)=P(x≤4)=
P(x≥1)=P(x≥1)=
P(1≤x≤3)=P(1≤x≤3)=
The shape of the probability distribution is Select an answer
uniform skewed left symmetric skewed right .
E)
The following table gives the frequencies of the nest size (number of eggs) of 199 Great Blue Heron nests recorded on a recent survey in Indian River County. Use the data to construct a discrete probability distribution.
| xx | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| ff | 7 | 45 | 50 | 34 | 20 | 43 |
Construct the probability distribution of xx, where xx is the number of eggs in a randomly selected Great Blue Heron nest in Indian River County. Round solutions to three decimal places, if necessary.
| xx | 0 | 1 | 2 | 3 | 4 | 5 |
| P(x)P(x) |
F)
A large fast-food restaurant is having a promotional game where
game pieces can be found on various products. Customers can win
food or cash prizes. According to the company, the probability of
winning a prize (large or small) with any eligible purchase is
0.116.
Consider your next 33 purchases that produce a game piece.
Calculate the following:
This is a binomial distribution. Round your answers to 4 decimal places.
a) What is the probability that you win 4 prizes?
b) What is the probability that you win more than 5 prizes?
c) What is the probability that you win between 3 and 5 (inclusive) prizes?
d) What is the probability that you win 3 prizes or fewer?
In: Statistics and Probability
Use a normal approximation to find the probability of the indicated number of voters. In this case, assume that 156 eligible voters aged 18-24 are randomly selected. Suppose a previous study showed that among eligible voters aged 18-24, 22% of them voted.
The probability that fewer than 37 voted
In: Statistics and Probability
Suppose that for a given computer salesperson, the probability distribution of x = the number of systems sold in 1 month is given by the following table.
| x | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| p(x) | 0.05 | 0.10 | 0.12 | 0.30 | 0.29 | 0.12 | 0.01 | 0.01 |
(a)
Find the mean value of x (the mean number of systems sold).
(b)
Find the variance and standard deviation of x. (Round your standard deviation to four decimal places.)
variance
standard deviation
How would you interpret these values? (Round your standard deviation to four decimal places.)
The mean squared deviation from the mean number of systems sold in one month is... . A typical deviation from the mean number of systems sold in one month is... .
(c)
What is the probability that the number of systems sold is within 1 standard deviation of its mean value?
(d)
What is the probability that the number of systems sold is more than 2 standard deviations from the mean?
In: Statistics and Probability
Let ? be the number of participants in a random meeting. The probability mass function of ? is given below. Assume that the meetings are independent.
0.5 for ? = 2
?(?) = 0.2 for ? = 4
0.3 for ? = 8
a) Find the mean and variance of ?.
b) What is the probability that the total number of participants in two meetings is exactly 10?
c) What is the probability that the number of participants in one meeting is fewer than 5?
d) What is the probability that the average number of participants in ten meetings is fewer than 5?
e) What is the probability that at least two out of ten meetings have less than 5 participants?
In: Statistics and Probability