Marks: 1

A bag of marbles contains 3 white and 4 black marbles. A marble will be drawn from the bag randomly three times and put back into the bag. Relative to the outcomes of the first two draws, the probability that the third marble drawn is white is:

Choose one answer.

Question54

Marks: 1

A parking lot has 100 red and blue cars in it.

• 40% of the cars are red.
• 70% of the red cars have radios.
• 80% of the blue cars have radios.

What is the probability that the car is red given that you already know that it has a radio?

Choose one answer.

Question55

Marks: 1

Which of the following methods produces a particularly stiff penalty in periods with large forecast errors?

Choose one answer.

Let D be the weight, in pounds, of a randomly selected male baseball player. Let L be the weight, in pounds, of a randomly selected female softball player. Suppose D is normally distributed with a mean weight of 173 pounds and a standard deviation of 29 pounds. Suppose L is normally distributed with a mean weight of 143 pounds and a standard deviation of 25 pounds. L and D are independent

a) Calculate the expected value of L + D. (in pounds)

b) Calculate the standard deviation of L + D. (in pounds)  

f) What is the probability that L + D is greater than 300 pounds?

g) Suppose we randomly select a male baseball player and a female softball player. What is the probability that each of these players weighs more than 150 pounds.? (L>150 and D>150)?

h)What is the probability that D is greater than L?

Suppose that, next month, the quality control division will inspect 80 units. Among these, 56 will undergo a speed test and 24 will be tested for current flow. If an engineer is randomly assigned 3 units, what are the probabilities that:

a) none of them will need a speed test?

b) only 2 will need a speed test?

c) at least 2 will need a speed test? Evaluate these solutions using the hypergeometric distribution and compare the result using the binomial distribution as an approximation.

Calculate the probability that the number 89 will come out when taking a ball from a bag with 120 balls numbered from 1 to 120.

Calculate the probability that "a number between 1 and 125" will come out when removing a ball from a bag with 130 balls numbered from 1 to 130.

If four questions with four options each are answered randomly, what is the probability of matching all of them?

Calculate the probability that "a number between 1 and 3" will come out when rolling a die.

If a die is rolled and the result is observed: What is the probability that a 6 does not come out?

Use the sample data and confidence level given below to complete parts​ (a) through​ (d). A research institute poll asked respondents if they felt vulnerable to identity theft. In the​ poll, n equals 922 and x equals 557 who said​ "yes." Use a 99 % confidence level.

According to a Yale program on climate change communication survey, 71% of Americans think global warming is happening.†

(a) For a sample of 16 Americans, what is the probability that at least 13 believe global warming is occurring? Use the binomial distribution probability function discussed in Section 5.5 to answer this question. (Round your answer to four decimal places.)

(b)For a sample of 170 Americans, what is the probability that at least 120 believe global warming is occurring? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.)

(c)As the number of trials in a binomial distribution application becomes large, what is the advantage of using the normal approximation of the binomial distribution to compute probabilities?

As the number of trials becomes large, the normal approximation gives a more accurate answer than the binomial probability function.As the number of trials becomes large, the normal approximation simplifies the calculations required to obtain the desired probability.    

(d)When the number of trials for a binomial distribution application becomes large, would developers of statistical software packages prefer to use the binomial distribution probability function shown in Section 5.5 or the normal approximation of the binomial distribution discussed in Section 6.3? Explain.

Consider a two-sided confidence interval for the mean μ when σ is known;

X̄-Zα1 σ/√n ≤ μ ≤ X̄+Zα2 σ/√n

where α1 + α2 = α. if α1= α2 = α/2, we have the usual 100(1-α)% confidence interval for μ. In the above, when α1 ≠ α2 , the interval is not symmetric about μ. Prove that the length of the interval L is minimized when α1= α2= α/2. Hint remember that Φ Zα = (1- α) , so Φ^-1 (1- α) = Zα, and the relationship between the derivative of a function y =f(x) and the inverse x=f^-1 (y) is (d/dy)f^-1 (y) = 1/ [d/dx f(x)] .

Problem 16-05 (Algorithmic)

A major traffic problem in the Greater Cincinnati area involves traffic attempting to cross the Ohio River from Cincinnati to Kentucky using Interstate 75. Let us assume that the probability of no traffic delay in one period, given no traffic delay in the preceding period, is 0.9 and that the probability of finding a traffic delay in one period, given a delay in the preceding period, is 0.75. Traffic is classified as having either a delay or a no-delay state, and the period considered is 30 minutes.

1. Assume that you are a motorist entering the traffic system and receive a radio report of a traffic delay. What is the probability that for the next 60 minutes (two time periods) the system will be in the delay state? Note that this result is the probability of being in the delay state for two consecutive periods. If required, round your answer to three decimal places.
   
   
   
2. What is the probability that in the long run the traffic will not be in the delay state? If required, round your answers to three decimal places.
   
   
   
3. An important assumption of the Markov process model presented here has been the constant or stationary transition probabilities as the system operates in the future. Do you believe this assumption should be questioned for this traffic problem? Explain.
   
   The input in the box below will not be graded, but may be reviewed and considered by your instructor.
   

Determine whether a probability model based on Bernoulli trials can be used to investigate the situation. If not, explain.

A company realizes that 5% of its pens are defective. In a package of 30 pens, is it likely that more than 6 are defective? Assume that pens in a package are independent of each other.

Group of answer choices

Yes

No. There are more than two possible outcomes.

No. 6 is more than 10% of 30

No, the chance of getting a defective pen changes depending on the pens that have already been selected.

No. The pens in a package are dependent on each other.

On an examination in Biochemistry  12 students in one class had a mean grade of 78 with a standard deviation of 6, while 15 students in another class had a mean grade of 74 with a standard deviation of 8. Using a significance level of 0.05, determine whether the first group is superior to the second group.

1) μ: $3600 per student σ: $150 Distribution: Skewed to the left Draw a well-labeled picture of the relevant sampling distribution for this population data including its standardization (z), assuming the sample size is 1700 school districts.

2) On average college students are given homework 3 nights a week. The 95% Confidence Interval is reported as 2 to 6 nights. Answer the following true or false, and correct the “false” statements.  

a.         T    F     The width of a Confidence Interval depends on the sample size.

b.         T    F     You can know for sure that this interval includes the true population

                        parameter.

c.         T    F     This Confidence Interval is interpreted to mean that 95% percent of all 8^th

                        graders in the district are given homework 2 to 6 nights a week.

d.         T    F     The purpose of a Confidence Interval is to provide a range of values which are

                        thought to include the sample mean.

Two types of solutions, A and B, were tested for their pH (degree of acidity of the solution). Analysis of 6 samples of A showed a mean pH of 6.72 with a standard deviation of 0.024. Analysis of 5 samples of B showed a mean pH of 6.49 with a standard deviation of 0.032. Using a 0.05 significance level, determine whether the two types of solutions have different pH values.

Although studies continue to show smoking leads to significant health problems, 30% of adults in a country smoke. Consider a group of 250 adults, and use the normal approximation of the binomial distribution to answer the questions below.

(a)What is the expected number of adults who smoke?

75  adults

(b)What is the probability that fewer than 65 smoke? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.)

(c)What is the probability that from 80 to 85 smoke? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.)

(d) What is the probability that 100 or more smoke? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.)

This question has been answered but the answers are incorrect

1. Suppose we have the following data on variable X (independent) and variable Y (dependent):

X         Y

2          70

0          70

4          130

1. By hand, determine the simple regression equation relating Y and X.
2. Calculate the R-Square measure and interpret the result.
3. Calculate the adjusted R-Square.
4. Test to see whether X and Y are significantly related using a test on the population correlation. Test this at the 0.05 level.
5. Test to see whether X and Y are significantly related using a t-test on the slope of X. Test this at the 0.05 level.
6. Test to see whether X and Y are significantly related using an F-test on the slope of X. Test this at the 0.05 level.