Question

Thirty four percent of businesses in a local community are located in the city's "Business District". If 17 businesses are randomly selected, what percentage chance that:

4 are located in the business district?

exactly 15 businesses are not located in the city's business district?

at most 1 business is located in the city's business district?

5 to 6 businesses are located in the city's business district?

Answer 1

Here, n = 17, p = 0.34, (1 - p) = 0.66 and x = 4
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 4)
P(X = 4) = 17C4 * 0.34^4 * 0.66^13
P(X = 4) = 0.1434

Here, n = 17, p = 0.66, (1 - p) = 0.34 and x = 15
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 15)

P(x = 15) = 17C15 * 0.66^15 * 0.34^2
= 0.0309

Here, n = 17, p = 0.34, (1 - p) = 0.66 and x = 1
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X <= 1).
P(X <= 1) = (17C0 * 0.34^0 * 0.66^17) + (17C1 * 0.34^1 * 0.66^16)
P(X <= 1) = 0.0009 + 0.0075
P(X <= 1) = 0.0084

Here, n = 17, p = 0.34, (1 - p) = 0.66, x1 = 5 and x2 = 6.
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(5 <= X <= 6)
P(5 <= X <= 6) = (17C5 * 0.34^5 * 0.66^12) + (17C6 * 0.34^6 * 0.66^11)
P(5 <= X <= 6) = 0.1921 + 0.1979
P(5 <= X <= 6) = 0.3900