Question

1 a) Maria answers 28 multiple-choice questions randomly guessing. 10 questions have 5 answer options, 15 questions have 6 answer options and 3 questions have 2 answer options. There is exactly one answer option for each problem. What is the expectation value of correct answers from Maria?

1. b) The pesticide content is adjusted so that 95% of the cabbage does not contain pests. What is the standard deviation of the number of pest cabbages in a random sample of 1000 cabbages? Give the answer as a whole number, rounded.

Thank you so much! I just need the answers for both a and b :)

Answer 1

1a)

Number of options	5	6	2
Number of questions (x)	10	15	3
Probability of correct answer p(x)

E(x) =

1b) This is binomial distribution.

SD =

Here n = 1000, p = 0.95 and q = 1-0.95 = 0.05

Rounded to the nearest whole number: SD = 7.