Question

Big babies: A public health organization reports that 30% of baby boys 6 - 8 months old in the United States weigh more than 20 pounds. A sample of 16 babies is studied. Round the answers to three decimal places.

Part 1 of 4

(a) What is the probability that exactly 6 of them weigh more than 20 pounds?

The probability that exactly 6 of them weigh more than 20 pounds is .

Part 2 of 4

(b) What is the probability that more than 5 weigh more than 20 pounds?

The probability that more than 5 weigh more than 20 pounds is .

Part 3 of 4

(c) What is the probability that fewer than 5 weigh more than 20 pounds?

The probability that fewer than 5 weigh more than 20 pounds is .

Part 4 of 4

(d) Would it be unusual if more than 4 of them weigh more than 20 pounds?

It ▼(Choose one) be unusual if more than 4 of them weigh more than 20 pounds, since the probability is .

Clears your work.

Undoes your last action.

Answer 1

p = 0.3

n = 16

P(X = x) =16Cx * 0.3^x * (1 - 0.3)^16-x

a) P(X = 6) = 16C6 * 0.3⁶ * 0.7¹⁰ = 0.1649

b) P(X > 5) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5))

                  = 1 - (16C0 * 0.3⁰ * 0.7¹⁶ + 16C1 * 0.3¹ * 0.7¹⁵ + 16C2 * 0.3² * 0.7¹⁴ + 16C3 * 0.3³ * 0.7¹³ + 16C4 * 0.3⁴ * 0.7¹² + 16C5 * 0.3⁵ * 0.7¹¹)

                  = 1 - 0.6598

                  = 0.3402

c) P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

                  = 16C0 * 0.3⁰ * 0.7¹⁶ + 16C1 * 0.3¹ * 0.7¹⁵ + 16C2 * 0.3² * 0.7¹⁴ + 16C3 * 0.3³ * 0.7¹³ + 16C4 * 0.3⁴ * 0.7¹²

                  = 0.4499

d) P(X > 4) = 1 - P(X < 4) = 1 - 0.4499 = 0.5501

It would not be unusual if more than 4 of them weigh more than 20 pounds, since the probability is not less than 0.05