If 44 bald eagles are randomly selected, find the probability that

Question

74% of all bald eagles survive their first year of life. Give your answers as decimals, not percents. If 44 bald eagles are randomly selected, find the probability that

a. Exactly 31 of them survive their first year of life. 

b. At most 33 of them survive their first year of life. 

c. At least 30 of them survive their first year of life. 

d. Between 30 and 34 (including 30 and 34) of them survive their first year of life. 

Answer 1

The random variable follows a Binomial Distribution with p=0.74 and n=44. I will show the TI84 calculator functions.

a. P(X=31) = ₄₄C₃₁ * 0.74³¹ * (1-0.74)¹³ = Binompdf(44,0.74,31) = 0.1138

b. P(X ≤ 33) = P(X = 0) + P(X = 1) + ...+ P(X= 33) = Binomcdf(44, 0.74, 33) = 0.6169

c. P(X ≥ 30) = 1 - PX ≤ 29 = 1 - Binomcdf(44, 0.74, 29) = 1 - 0.1468 = 0.8532

d. P(30 ≤ X ≤ 34) = P(X ≤ 34) - P(X ≤ 29) = Binomcdf(44, 0.74, 34) - Binomcdf(44, 0.74, 29)

= 0.7423 - 0.1467

= 0.5955

Let me know if you have any questions or if you use a different statistics calculator or software.