1. Which of the following random variables, X, is a binomial random variable? A
ID: 3327775 • Letter: 1
Question
1. Which of the following random variables, X, is a binomial random variable?
A X is the number of hearts when 4 cards are dealt without replacement from a standard deck of cards.
B X is the number of voters from a random sample of 78 voters in a town who plan to vote against a proposition to increase spending on public schools.
C X is the number of rainy days in Columbus, Ohio.
D X is the number of students who received A, B or C grade from a statistics class with 25 students.
2. If IQ scores are normally distributed with a mean 100 and a standard deviation 15, what is the IQ score that marks the top 10%, rounded to nearest whole number?
A) 81 B) 99 C) 119 D) 110
3. If a population has a mean µ=12 and a standard deviation =2.4, which of the following correctly gives the values of and , for samples of size n=64?
A) =1.5 B) =12 C) =1.5 D) =12
=2.4 =0.038 =0.3 =0.3
(10 points – 2 pts each) The Student Learning Center of Franklin University surveyed students to see how many times per week each visited SLC in a trimester. The following table shows the number of visits to SLC, X, per week students had and their probabilities.
X = # of visits
P(x)
3
0.10
4
0.23
5
0.30
6
0.27
7
0.10
Answer the following questions using the information above.
What is the probability that a student visited SLC more than 4 times a week?
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What is the probability that a student visited SLC at least 6 times a week?
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What is the probability that a student visited SLC at most 4 times a week?
_________________________________________________________________
What is the expected value of X? Interpret it.
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Give at least two reasons to explain why this is a valid probability distribution:
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(12 points – 2 pts each) Historical data shows that 63% of students enrolled in a Math class at a local university during any term pass the course. A random sample of 24 students has been taken. Answer the following questions based on this scenario. (Show the formula or the calculator command that you use as appropriate). Round your answers to 3 decimal places.
What type of probability distribution applies to this problem? Show that it satisfies the criteria of this probability distribution.
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Find the probability that exactly 16 students in this section will pass this term. Would that be an unusual probability?
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Find the probability that at most 11 students pass the course this term.
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Find the probability that at least 7 students pass the course.
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Find the expected number of students who will pass the course this term. i.e. the expected value of this probability distribution.
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Find the standard deviation of the number of students who will pass the course this term. i.e. the standard deviation of this probability distribution.
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(10 points – 2 pts each) Alana works as a production manager at a company. Recently, she has been charged by her supervisor to determine how much time employees spend to complete a certain spreadsheet task. In order to answer this question, she randomly selected 20 employees in the company and recorded their time in minutes to complete this task. Her data is summarized below. Assume that the distribution of completion times is approximately normal.
Find the point estimate for µ, the mean amount of completion time for the task.
Construct a 95% confidence interval for the population mean time to complete this task. Show your work or calculator command.
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Interpret this interval in the context of the problem. Use complete sentences.
What is the margin of error?
An employee claims that she is used to working with spreadsheets and she can complete this task in 11.5 minutes. Does this contradict your findings above? Justify your answer and be specific.
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(10 points – 2 pts each) A survey of first year students at Franklin University revealed that the number of hours spent studying the week before final exams was normally distributed with mean 25 hours and standard deviation 7 hours. Show your work or calculator commands to answer the following questions. (You may use the space in the margin to sketch curves to help you answer the questions)
What percent of Franklin University first year students studied less than 18 hours the week before the final exams?
Eighty percent of Franklin University first year students studied less than what number of hours in the week before the final exams?
What is the probability that a randomly selected Franklin University first year students studied more than 30 hours in the week before the final exams?
For a random sample of 16 Franklin University first year students, what is the probability that the sample mean study time in the week before the final exams is more than 30 hours?
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Determine if either of the probabilities you found in parts C) or D) is an unusual probability. Justify your answer.
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(10 points – 2 pts each) Answer the following questions using the standard normal distribution:
Write the values of the following about the standard normal distribution:
Mean __________________ ii. Standard deviation _________________
What is the probability that a z-score is between -1.2 and 1.74? _________________
What percent of data is more than z=1.56? _________________________
What z-score represents the 45th percentile? _______________________
What is the value of Z0.75? ______________________________
(11 points) According to a recent National Health Statistics Report, the weights of male babies less than two months old in the United States are normally distributed with a mean 11.5 pounds and a standard deviation 2.7 pounds. A sample of 49 male babies, who were less than two months old, was randomly selected and found to have a sample mean weight of 12.1 pounds and standard deviation of 2.3 pounds.
Answer the following questions based on this scenario.
Question
Symbol
Numeric Value
(1 pt) What is the population mean?
(1 pt) What is the population standard deviation?
(1 pt) What is the sample mean?
(1 pt) What is the sample standard deviation?
(1 pt) What is the sample size?
(2 pts) When samples of 49 male baby weights are selected from this population, what is the mean of the sampling distribution of sample means?
(2 pts) When samples of 49 male baby weights are selected from this population, what is the standard deviation of the sampling distribution of sample means?
(2 pts) Explain whether the sampling distribution is normal.
(12 points) The Human Resources Department of a large manufacturing company wants to estimate the proportion of employees who have received CPR training. Based on a simple random sample of 150 employees, it was found that 48 have CPR training. It is desired to construct a 98% confidence interval for the proportion of all employees who have CPR training. Answer the following questions. Show your work or your calculator commands.
(2 pts) Find the point estimate, , of the population proportion.
(2 pts) Find the critical value of the confidence interval.
(2 pts) Find the margin of error of the confidence interval.
(3 pts) Construct a 98% confidence interval for the proportion of all employees who have CPR training.
_____________________________
(3 pts) If the Human Resources Department wants to keep the margin of error at 0.04 for the 98% confidence interval, what size of sample should be taken?
____________________________
(5 points – 1 pt each) Mark the following statements as True (T) or False (F).
_____In a normal quantile plot, if the points do not closely follow a straight line, the
distribution is considered not to be normal.
_____ The sampling distribution of sample means shows the distribution of all the data in
all the samples.
_____ If we increase the sample size for a confidence interval at a given confidence
level, this would decrease the margin of error.
_____ The Empirical Rule applies to any probability density curve.
_____ For a sample size larger than 30, the mean of the sampling distribution of sample
means is equal to the population mean.
X = # of visits
P(x)
3
0.10
4
0.23
5
0.30
6
0.27
7
0.10
Explanation / Answer
1) B. X is the number of voters from a random sample of 78 voters in a town who plan to vote against a proposition to increase spending on public schools.
The trials are finite(78 times), Only 2 outcomes possible and the probability for each trial remains same.
2) P(z = (x - 100)/15) = 0.9
(x-100)/15 = 1.282 , x = 119.23 (Option C)
Question 3 is not complete. few characters are missing
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