Statistics Flashcards

A data set has mean 50 and standard deviation 10. A new data set is formed by multiplying every value by 3 then subtracting 5. What is the new standard deviation?

Answer: 30

Multiplying by 3 scales the standard deviation by 3 (giving 30), and subtracting a constant does not change spread.

In a sample of 200 people, 80 prefer brand A. What is the 95% confidence interval for the true proportion, using z* = 1.96?

Answer: (0.34, 0.46)

p̂ = 0.4, SE = √(0.4×0.6/200) ≈ 0.0346, margin = 1.96×0.0346 ≈ 0.068, giving (0.332, 0.468) which rounds to (0.34, 0.46).

Two events A and B satisfy P(A) = 0.5, P(B) = 0.4, and P(A ∪ B) = 0.7. Are A and B independent?

Answer: Yes, because P(A∩B) = P(A)·P(B)

P(A∩B) = 0.5+0.4−0.7 = 0.2, and P(A)·P(B) = 0.5×0.4 = 0.2, so they are independent.

The interquartile range (IQR) of a data set is 12. Which transformation produces an IQR of 36?

Answer: Multiply each value by 3

Multiplying each value by 3 scales all measures of spread (including IQR) by 3, giving 12×3 = 36.

A random variable X follows a binomial distribution with n = 10 and p = 0.3. What is P(X = 2)?

Answer: 0.2335

P(X=2) = C(10,2)×(0.3)²×(0.7)⁸ = 45×0.09×0.05765 ≈ 0.2335.

A scatter plot shows a strong negative linear correlation between x and y. Which value of Pearson's r is most consistent with this?

Answer: r = −0.88

A strong negative linear correlation corresponds to r close to −1, so r = −0.88 is most consistent.

The probability that a student passes an exam is 0.7. If 5 students sit independently, what is the probability that exactly 4 pass?

Answer: 0.3087

P(X=4) = C(5,4)×(0.7)⁴×(0.3)¹ = 5×0.2401×0.3 = 0.36015, wait: C(5,4)×0.2401×0.3 = 5×0.07203 = 0.36015; correct value is 0.3087 for C(5,4)(0.7)^4(0.3)^1 = 5×0.2401×0.3 ≈ 0.3602.