Question

Popol street bikes are displayed in chic clothing boutiques in Paris, France, and the average price for the bike in the city is $700. Supose that the variance of bike prices is $28,651. if a random sample of 60 boutiques is selected, what is the probability that the average price for Popol street bike in this sample will be between $680 and $720?

a. 0.6407

b. 0.0043

c. 0.0054

d. 0.9167

Answer 1

Let X denote the price of the bike in the city

E(X) = 700

Var(X) = 28651

=> sd(x) = (28651)^{^0.5} = 169.3

Let (X₁ , X₂ , ... , X₆₀ ) be a random sample of size 60

Using C.L.T we know that

We want to find the probability that the average price for Popol Street bike in this sample will be between $680 and $720.