Question

# Let X represent a binomial random variable with n = 170 and p = 0.6. Find...

Let X represent a binomial random variable with n = 170 and p = 0.6. Find the following probabilities. (Do not round intermediate calculations. Round your final answers to 4 decimal places.)

Probability

a.P(X ≤ 100)

b.P(X > 110)

c.P(105 ≤ X ≤ 115)

d.P(X = 90)

(A) To find Using binomcdf(n,p,k)

it is given that n = 170, p=0.6 and k = 100

= binomcdf(170,0.6,100)

= 0.4053

Therefore, = 0.4053

(B) To find Using P(x more than 110)= 1 - binomcdf(n,p,k)

it is given that n = 170, p=0.6 and k = 110

= 1 - binomcdf(170,0.6,110)

= 1 - 0.9091

= 0.0909

Therefore, = 0.0909

(C) To find We can write it as this implies = binomcdf (170,0.6,115) - binomcdf ( 170, 0.6, 105-1)

= binomcdf (170,0.6,115) - binomcdf ( 170, 0.6, 104)

= 0.9837 - 0.6505

= 0.3332

Therefore, = 0.3332

(D) To find P(x = 90)

Using binompdf(n,p,k)

it is given that n = 170, p=0.6 and k = 90

= binompdf(170,0.6,90)

= 0.0108

Therefore,P(x=90) = 0.0108

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