Consider a binomial probability distribution with pequals=0.6 and nequals=8

Determine the probabilities below.

1)Upper P left parenthesis x equals 2 right parenthesisP(x=2)

2)Upper P left parenthesis x less than or equals 1 right parenthesisP(x≤1)

3)Upper P left parenthesis x greater than 6 right parenthesisP(x>6)

(1) The probability of the event X = 2 is 0.0413.

(2) The probability of the event X ≤ 1 is 0.009.

(3) The probability of the event X < 6 is 0.6846.

Step-by-step explanation:

Let the random variable X follow a Binomial distribution with parameter n = 8 and p = 0.60.

The probability mass function of the Binomial distribution is:

(1)

Compute the probability of the event X = 2 as follows:

Thus, the probability of the event X = 2 is 0.0413.

(2)

Compute the probability of the event X ≤ 1 as follows:

P (X ≤ 1) = P (X = 0) + P (X = 1)

Thus, the probability of the event X ≤ 1 is 0.009.

(3)

Compute the probability of the event X < 6 as follows:

P (X < 6) = 1 - P (X ≥ 6)

              = 1 - P (X = 6) - P (X = 7) - P (X = 8)

   

Thus, the probability of the event X < 6 is 0.6846.

The second one and the forth one.

The second one because it is true that half of the diameter is the radius.

The forth one because is you do 2 x pi x 31.4 = 197.29 divide that by pi and you get 62.8 pi.

The only reason it is not the third one is because it does not have the step to divide 197.29 by pi.

Hope this Helps!!