Question

You've been having some trouble sleeping. If there's an 80% chance that you sleep at least 8 hours in a night, what's the probability (to the nearest hundredth) that you will be able to get at least 8 hours of sleep for 3 or more nights in a given week? a) 0.28 b) 0.39 c) 0.43 d) 0.57 e) Answer is not there

Answer 1

1. P(you sleep at least 8 hours), p = 0.8

q = 1 - p = 0.2

Sample size, n = 7 (7 days of a week)

Binomial distribution: P(X) = nCx p^x q^n-x

P(at least 8 hours of sleep for 3 or more nights in a given week) = 1 - P(at least 8 hours of sleep for less than 3 nights in a given week)

= 1 - [P(0) + P(1) + P(2)]

= 1 - [0.2⁷ + 7x0.8x0.2⁶ + 7C2x0.8²x0.2⁵]

= 1 - 0.005

= 0.995

Ans: Answer is not there

2. We have to find the distance between the given point and the correlation line. The one which is closest to the line will have least impact if moved.

Distance corresponding to (1,4) = 4 - 2 = 2

Distance corresponding to (3,2) = 4 - 2 = 2

Distance corresponding to (0.5, 2.5) = 2.5 - 1.5 = 1

Distance corresponding to (2, 0.5) = 2.5

Ans: b) (0.5, 2.5)