Midterm 2 Questions

Where is the 10th percentile of the Z distribution?

-1.28

Use the following probability distribution to find the probability that X is exactly 6. X 3 6 9 P(x) 0.45 0.40 0.15

0.40

Suppose X has a continuous random variable with the pdf defined as below: f(x) = 1/9x^2 0 < x < 3 What is the probability that x is greater than 2

0.7

X is a normally distributed random variable with mean 50 and standard deviation 5. What is the probability that 2X will be less than 110?

0.841

If X has a continuous uniform distribution on the interval (0,5), what is the 25th percentile for X?

1.25

If X has a continuous uniform distribution on the interval (50, 100), then what is f(75)?

1/50

Suppose X has a continuous random variable with the pdf defined as below: f(x) = 1/9x^2 0 < x < 3 What is the mean of X?

2.25

Suppose 20% of Ohio residents support the legalization of marijuana. If you randomly select n people and would like to use the normal approximation to answer questions, what does your sample size have to be, at minimum?

50

If the Z-score is 1.96, and X has a normal distribution with mean 60 and standard deviation 6, what X-value corresponds to this Z-score?

71.76

Suppose 40% of college students plan to vote in the election. Now suppose we randomly select 200 college students and ask them if they plan to vote. What is the probability that more than 75 of the 200 students sampled plan to vote?

76.4%

The time (X) to complete a standardized exam is approximately normal with a mean of 70 minutes and standard deviation of 10 minutes. How much time should be given to complete the exam so that 80% of the students will complete the exam in the time given?

78.4 minutes

Suppose someone claims the average delivery time for U.S. packages to be delivered during December is 2 days. You believe it takes longer than that. You conduct a hypothesis test; what are your hypotheses?

Ho: µ = 2 vs. Ha: µ >2

When you are asked to provide a range of likely values for the average gas price in Columbus Ohio, what technique do you use?

confidence interval for the population mean

Which of the following variables is binomially distributed?

flipping a coin 10 times

Suppose you found a 95% confidence interval for the mean using a random sample of size n, and you found it was too wide; that is, the margin of error was too large. If you wanted the margin of error to be ¼ of what it was before, what do you have to do to the sample size?

increase it by 16 times what it was before

The set of all possible sample means from all possible samples of size n from the population is known as the:

sampling distribution of x bar

A company has developed a new battery, but the average lifetime of all of the batteries it makes is unknown. In order to estimate this average, a sample of 500 batteries is tested and the average lifetime of this sample is found to be 225 hours. The 225 hours is the value of a:

statistic

Which of the following is true about the mean of the random variable X-bar as n increases?

the mean of x bar stays the same

The Central Limit theorem tells us important results that pertain to:

the shape (type) of the distribution of x bar

The p-value will change if you get a new data set.

true

If your 95% confidence interval for the average gas price in Columbus Ohio turned out to be ($2.25, $2.75), do you know what the sample mean was?

yes

Suppose X has a normal distribution with mean 10 and standard deviation 2. In order for the Z-score to be equal to 0, then X must be equal to

10

What is the value of (5 2)?

10

The value of α will change if you get a new data set.

false

A binomial random variable is what type of random variable?

discrete random variable

Which of the following would increase the Margin of Error?

increase the confidence

How large does n generally have to be in order for the Central Limit Theorem to take effect? (Assume X does not have a normal distribution.)

n>30

Which of the following is NOT a condition of the binomial distribution?

none of the above: set number of trials two outcomes (yes or no) independent trials fixed probability (p)

If X is a random variable with standard deviation 15, then the standard deviation of 2X is 30.

true

The margin of error of a confidence interval increases if the population has a higher standard deviation.

true

If X is a binomial random variable with n = 4 and p = 0.18. What is P(X = 3)?

0.019

If an observation has a z-score of -1.5, how many standard deviations is it above or below the mean?

1.5 standard deviations below the mean

The national proportion of adults who are concerned about nutrition is 0.4. You take a random sample of 10 adults and count the number who are concerned about nutrition (call it X). What is the probability that X is at least 2?

0.9537

If X does not have a normal distribution, which of the following is true about the shape (distribution) of the random variable X-bar?

X-bar is approximately normal if n > 30

Is the following a legitimate discrete probability distribution? X 3 6 9 P(x) .45 .40 .15

Yes, because P(x) is between 0 and 1 for all possible values of X. Yes, because the total probablity of X sums to 1.

The Normal distribution is an example of a _________________ Distribution.

continuous

The number of injuries sustained by an entire football team during a typical college football game is a discrete random variable.

true

If X is a continuous random variable, which of the following conditions does NOT need to be checked to verify that f(x) is a legitimate probability distribution function?

f(x) must be less than or equal to 1

If X has a uniform distribution with f(x)=1/10 we know the values of X MUST go from 0 to 10; they can be no where else.

false

If X is a binomial random variable with n = 15 and p = 0.3, we can use the normal approximation.

false

If X is binomial with n = 5 and p = 0.05, the chance that X is at least 1 is 0.6240

false

Suppose X has a distribution with mean 10 and variance 4, Y has a distribution with mean 20 and variance 9. We do not know whether X and Y are independent. However, we CAN still find the variance of X+Y with only the information we are given.

false

The time to complete a standardized exam is approximately normal with a mean of 70 minutes and a standard deviation of 10 minutes. The percentage of the students which take longer than 80 minutes to complete the exam is 84.13%.

false

What is the symbol we use to represent the mean of the random variable X-bar?

mu with subscript x bar

Which of the following is true about the standard error of the random variable X-bar as n increases?

the standard error of x bar decreases

If everything else stays the same, a 90% confidence interval is narrower than a 95% confidence interval.

true

For a normally distributed variable X with mean 40 and standard deviation 10, what is the probability that X equals exactly 30? In notation, what is P(x=30)

0

If X has a continuous uniform distribution on the interval (50, 100), then what is P(X=75)?

0

What is the probability that a normally distributed random variable X is greater than 85 if μX=75 σX=4?

0.006

Suppose X has a distribution with mean 10 and variance 4, Y has a distribution with mean 20 and variance 9. You can find the mean of X + Y with this information.

true

Your friend claims the average price of a burger in the Columbus Gateway Area is $10.00. You believe it's lower than that. What symbol represents the $10 in this scenario?

u0

Which of the following describes the relationship between parameters and statistics?

we use statistics to estimate or test parameters

If X has a normal distribution, which of the following is true about the shape (distribution) of the random variable X-bar?

x bar is exactly normal for any n

Suppose X is the number of cars that a family owns, and that X has the following probability distribution. X 0 1 2 P(x) 0.05 0.39 0.56 Suppose you choose two families at random. What is the chance that family A owns exactly one car and family B owns exactly one car?

0.1521

For the discrete probability distribution below, the variance of X is 5.4 units. X 3 6 9 P(x) 0.45 0.40 0.15

False

Use the probability distribution below to find the probability that X is 6 or greater. X 3 6 9 P(x) 0.45 0.40 0.15

0.55

Suppose X is the number of cars that a family owns, and that X has the following probability distribution. X 0 1 2 P(x) 0.05 0.39 0.56 What is the chance that family owns more than one car?

0.56

For the discrete probabilty distribution below, the mean of X is 6 units. X 3 6 9 P(x) 0.45 0.40 0.15

False

If X and Y are independent, then Variance of X-Y = Variance of X - Variance of Y

False