Question

I observed whether or not passers-by in front of my house observed the 6 foot social distance requirement. I recorded a 1 if the passer-by observed the rule and a 0 if the passer-by did not observe the rule. Here is the tally for a sample of 8 passers-by. 1 1 0 0 0 0 1 0.

You may treat this tally as a sample from a distribution of binary choices people make on my street.

Using the data from the introduction, what is the probability that 6 or more passers-by will observe the 6 foot social distancing rule?

Select one:

a. From about 96.55 per cent

b. About 37.5 per cent

c. About 3.6 per cent

d. About 62.5 per cent

Answer 1

From given tally for a sample of 8 passers-by, we get 3 passer-by observed the rule.

Therefore, P(observed rule) = p = 3/8 = 0.375

q = 1 - p = 1 - 0.375 = 0.625

Let X be a number of passers-by will observe the 6 foot social distancing rule among 8 passers-by.

Here, X ~ Binomial (n = 8, p = 6)

We want to find, P(X ≥ 6)

=> P(X ≥ 6) = 0.036 (OR 3.6%)

Answer : c) About 3.6 percent