It is reported that 77% of workers aged 16 and over drive to work alone. Choose 8 workers at random. If X represents the random variable of driving to work alone, the following table depicts the probabilities for this case.

Find the following probabilities as percentages to 1 d.p.

a) Probability that none drives to work alone

b)Probability that exactly 5 drive to work alone

c)Probability that at most 4 drive to work alone.

Guest Apr 15, 2020

#1**+1 **

Probability of driving to work alone = 0.77

Probability of not driving to work alone = 0.23

Total number of workers = 8

Probability that none drive to work alone: _{8}C_{0}·(0.77)^{0}·(0.23)^{8} =

Probability that exactly 5 drive to work alone: _{8}C_{5}·(0.77)^{5}·(0.23)^{3} =

Probability that at most 4 drive to work alone: [this would be either 4 or 3 or 2 or 1 or none of them]

_{ = 8}C_{4}·(0.77)^{4}·(0.23)^{4} + _{8}C_{3}·(0.77)^{3}·(0.23)^{5} + _{8}C_{2}·(0.77)^{2}·(0.23)^{6} + _{8}C_{1}·(0.77)^{1}·(0.23)^{7} + _{8}C_{0}·(0.77)^{0}·(0.23)^{8} =

geno3141 Apr 15, 2020