problem 1-6, please solve multiple-choice, no work needed.

I) Which of the following statements is NOT true regarding a normal distribution?

A. A normal distribution has two parameters, its expected value and variance/standard deviation.

B. In a normal distribution, it is less likely to observe values closer to its expected value than in the tails.

C. The probability density function of a normal distribution is symmetric and bell-shaped.

D. Any normal distribution can be transformed to a standard normal distribution.

II) Let Z ~ Norm(0, 1) and Y ~ t_n (i.e. a t-distribution onndegrees of freedom).

Which of the following statements is true?

A. Pr(Z< 0) < Pr(Y < 0)

B. Pr(Z< 0) > Pr(Y < 0)

C. Pr(Z< 0) = Pr(Y < 0)

D. It cannot be determined with only the information given

III) When implementing a two-sided z-test for a population mean,. The standardized

test statistic follows which of the following distributions when the Null hypothesis is true?

A.Norm(₀, ²), where ₀ is the null value

B. Norm(0, 1)

C. t_n

D. An s-distribution

IV) If two events, E and F, are independent, then this implies which of the following?

A.Pr(E F) = Pr(E) + Pr(F)

B.Pr(E F) = Pr(E) + Pr(F)

C.Pr(E F) = Pr(E) Pr(F)

D.Pr(E F) = Pr(E) Pr(F)

V) In a box plot, which of the statements below is true? ____

A. The line inside the box represents the mean and the two ends of the box represent the lower and upper quartile.

B. The line inside the box represents the median and the two ends of the box represent 1.5 times the inter-quartile range from the median.

C. The line inside the box represents the median and the two ends of the box represent the lower and upper quartile.

D. The line inside the box represents the mean and the two ends of the box represent 1.5 times the inter-quartile range from the mean.

VI) Which of the following is the correct frequentist interpretation of a (1 -a₀)% confidence interval for some parameter of interest?

A.The probability the parameter of interest falls within the confidence interval isa₀

B.The probability the parameter of interest falls within the confidence interval is(1 -a₀)

C.The probability the confidence interval covers the true value of the parameter is(1 -a₀)

D.The probability the confidence interval covers the true value of the parameter isa₀