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
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
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
art 2 The mean number of accidents at a certain intersection is about five. Find the...
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