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.

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