Question 1:
Suppose a baseball player had 223 hits in a season. In the given probability distribution, the random variable X represents the number of hits the player obtained in a game.
| x |
P(x) |
| 0 |
0.1844 |
| 1 |
0.3902 |
| 2 |
0.2379 |
| 3 |
0.0953 |
| 4 |
0.0489 |
| 5 |
0.0433 |
(a) Compute and interpret the mean of the random variable X.
μx =
(Round to one decimal place as needed.)
Question 2:
If we consider an experiment of generating 196 births and recording the genders of the babies, the mean number of girls is 98 and the standard deviation is 7 girls. Would it be unusual to get 110 girls in 196 births? Why or why not?
Choose the correct answer below.
A. No, because 110 is below the minimum usual value.
B. Yes comma because 110 is greater than the maximum usual value.
C. Yes, because 110 is within the range of usual values.
D. No comma because 110 is within the range of usual values.
Question 3:
Let the random variable x represent the number of girls in a family with three children. The probability of a child being a girl is 0.36. Construct a table describing the probability distribution, then find the mean and standard deviation. Is it unusual for a family of three children to consist of three girls?
Find the probability of a family having x girls out of 3 children.
x P(x)
0 ___
1 ___
2 ___
3 ___
(Round to three decimal places as needed.)
Question 4:
Determine whether the following probability experiment represents a binomial experiment and explain the reason for your answer.
An experimental drug is administered to 50 randomly selected individuals, with the number of individuals responding favorably recorded.
Does the probability experiment represent a binomial experiment?
A. No, because the probability of success differs from trial to trial.
B. No, because the trials of the experiment are not independent.
C. Yes, because the experiment satisfies all the criteria for a binomial experiment.
D. No, because there are more than two mutually exclusive outcomes for each trial.
Question 5:
Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial.
n=6, x=4, p=0.55
Question 6:
Refer to the Minitab display to the right. The probabilities were obtained by entering the values of n=5 and p=0.146. In a clinical test of a drug, 14.6% of the subjects treated with 10 mg of the drug experienced headaches. In each case, assume that 5 subjects are randomly selected and treated with 10 mg of the drug. Find the probability that at least four of the subjects experience headaches.
| x |
P(X=x) |
| 0 |
0.4542 |
| 1 |
0.3883 |
| 2 |
0.1328 |
| 3 |
0.0227 |
| 4 |
0.0019 |
| 5 |
0.0001 |
Question 7:
Assume that a procedure yields a binomial distribution with n trials and the probability of success for one trial is p. Use the given values of n and p to find the mean μ and standard deviation σ. Also, use the range rule of thumb to find the minimum usual value μ-2σ and the maximum usual value μ+2σ.
n=1590, p= 4/5
Question 8:
Assume the readings on thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. Find the probability that a randomly selected thermometer reads greater than 0.91 and draw a sketch of the region.
Refer the attached table
Sketch the region. Choose the correct graph below.
Question 9:
Assume the readings on thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. Find the probability that a randomly selected thermometer reads between negative -0.53 and 0.53 and draw a sketch of the region.
Sketch the region. Choose the correct graph below.
Question 10:
Assume the readings on thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. Find the probability P(-0.99P(-0.99
Question 11:
Assume that the readings on the thermometers are normally distributed with a mean of 0° and standard deviation of 1.00°C. A thermometer is randomly selected and tested. Draw a sketch and find the temperature reading corresponding to Upper P95, the 95%. This is the temperature reading separating the bottom 95% from the top 5%.
Refer the attached table
Which graph represents Upper P95? Choose the correct graph below.
Question 12:
Find the indicated IQ score. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.
Refer the attached table
The indicated IQ score, x, is __.
Question 13:
Assume that adults have IQ scores that are normally distributed with a mean of μ=100 and a standard deviation σ=20. Find the probability that a randomly selected adult has an IQ less than 140.
Refer the attached table
The probability that a randomly selected adult has an IQ less than 140 is __.
Question 14:
Men's heights are normally distributed with mean 68.7 in and standard deviation of 2.8 in. Women's heights are normally distributed with mean 63.2 in and standard deviation of 2.5 in. The standard doorway height is 80 in.
Refer the attached table
a. What percentage of men are too tall to fit through a standard doorway without? bending, and what percentage of women are too tall to fit through a standard doorway without bending?
b. If a statistician designs a house so that all of the doorways have heights that are sufficient for all men except the tallest 5%, what doorway height would be used?
a. The percentage of men who are too tall to fit through a standard door without bending is __.
Question 15:
What is the standard error of the mean?
Choose the correct answer below.
A. The variance of the sample means.
B. The mean of the sample means.
C. The standard deviation of the sample means.
D. The range of the sample means.
Question 16:
Use the continuity correction and describe the region of the normal distribution that corresponds to the indicated probability. For example, the probability of "more than 20 defective items" corresponds to the area of the normal curve described with this answer: "the area to the right of 20.5."
The probability of no more than 9 students in a class
Attachment:- data.xlsx