Question

art 2 The mean number of accidents at a certain intersection is about five. Find the probability that the number of accidents at this certain intersection on any given day is

1. exactly seven,

2. at least six,

3. no more than four.

Part 3. Thirty-eight percent of adults say that Google news is a major source of new for them. You randomly select 17 adults. Find the probability that the number of adults who say that Google news is a major source of new for them is

1. exactly three,

2. more than six,

3. at most nine.

Answer 1

2)

a)

Here, λ = 5 and x = 7
As per Poisson's distribution formula P(X = x) = λ^x * e^(-λ)/x!

We need to calculate P(X = 7)
P(X = 7) = 5^7 * e^-5/7!
P(X = 7) = 0.1044

b)

Here, λ = 5 and x = 6
As per Poisson's distribution formula P(X = x) = λ^x * e^(-λ)/x!

We need to calculate P(X > =6) = 1 - P(X <= 5).
P(X >=6) = 1 - (5^0 * e^-5/0!) + (5^1 * e^-5/1!) + (5^2 * e^-5/2!) + (5^3 * e^-5/3!) + (5^4 * e^-5/4!) + (5^5 * e^-5/5!)
P(X > 5) = 1 - (0.0067 + 0.0337 + 0.0842 + 0.1404 + 0.1755 + 0.1755)
P(X > =6) = 1 - 0.616

= 0.3840

c)

Here, λ = 5 and x = 4
As per Poisson's distribution formula P(X = x) = λ^x * e^(-λ)/x!

We need to calculate P(X < 4).
P(X < 4) = (5^0 * e^-5/0!) + (5^1 * e^-5/1!) + (5^2 * e^-5/2!) + (5^3 * e^-5/3!)
P(X < 4) = 0.0067 + 0.0337 + 0.0842 + 0.1404
P(X <4) = 0.2650

3)

a)

Here, n = 17, p = 0.38, (1 - p) = 0.62 and x = 3
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 3)
P(X = 3) = 17C3 * 0.38^3 * 0.62^14
P(X = 3) = 0.0463

b)

Here, n = 17, p = 0.38, (1 - p) = 0.62 and x = 6
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X > 6).
P(X <= 6) = (17C0 * 0.38^0 * 0.62^17) + (17C1 * 0.38^1 * 0.62^16) + (17C2 * 0.38^2 * 0.62^15) + (17C3 * 0.38^3 * 0.62^14) + (17C4 * 0.38^4 * 0.62^13) + (17C5 * 0.38^5 * 0.62^12) + (17C6 * 0.38^6 * 0.62^11)
P(X <= 6) = 0.0003 + 0.0031 + 0.0151 + 0.0463 + 0.0993 + 0.1582 + 0.1939
P(X <= 6) = 0.5162

P(x> 6) = 1 - P(x< =6)
= 1 - 0.5162
= 0.4838

c)

Here, n = 17, p = 0.38, (1 - p) = 0.62 and x = 9
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X <= 9).
P(X <= 9) = (17C0 * 0.38^0 * 0.62^17) + (17C1 * 0.38^1 * 0.62^16) + (17C2 * 0.38^2 * 0.62^15) + (17C3 * 0.38^3 * 0.62^14) + (17C4 * 0.38^4 * 0.62^13) + (17C5 * 0.38^5 * 0.62^12) + (17C6 * 0.38^6 * 0.62^11) + (17C7 * 0.38^7 * 0.62^10) + (17C8 * 0.38^8 * 0.62^9) + (17C9 * 0.38^9 * 0.62^8)
P(X <= 9) = 0.0003 + 0.0031 + 0.0151 + 0.0463 + 0.0993 + 0.1582 + 0.1939 + 0.1868 + 0.1431 + 0.0877
P(X <= 9) = 0.9338