Question

1) A single card is drawn from a standard 52 card deck. Calculate the probability that a black card or an ace is drawn. (show answer as a reduced fraction #/#)

2)A professor knows from past experience that in a class of 36 students the time for students to complete an exam has an N(50,10) distribution. Suppose that he wants to allow sufficient time so that 98% of the students will complete the exam in the allotted time. How much time should he allow for the exam? (Round to the whole number)

3)

Suppose we are testing the null hypotheses H₀: μ=118 against H_a: μ≠118. Suppose our population is normal with a standard deviation of 12. A random sample of 50 observations are drawn from the population, and we find the sample mean of these observations is 120.

a. Find the P-value is (Round to two decimals throughout and show answer as a percent with two decimals)

b.If α= .10, should we accept H₀ or H_a?  (Show answer as Ho or Ha)

Answer 1

Note: Question 2 does not specify whether 10 is a variance or standard deviation. Ideally it should be variance, nut I have performed it considering both the cases. Please check and use the solution accordingly.