Question

If an orange tree sapling is planted, it has a 70% chance of growing into a healthy and productive tree. If 20 randomly selected saplings are planted, answer the following. Use technology or the binomial probability table to calculate the following probabilities. Round solutions to four decimal places, if necessary.

a) What is the probability that exactly 15 of them grow into a healthy and productive tree?

P(x=15)=

b) What is the probability that less than 15 of them grow into a healthy and productive tree?

P(x<15)=

c) What is the probability that more than 15 of them grow into a healthy and productive tree?

P(x>15)=

d) What is the probability that exactly 16 of them grow into a healthy and productive tree?

P(x=16)=

e) What is the probability that at least 16 of them grow into a healthy and productive tree?

P(x≥16)=

f) What is the probability that at most 16 of them grow into a healthy and productive tree

P(x≤16)=

Answer 1

P( Sapling will grow into a healthy and productive tree) =0.7 =p

n= 20

Let X be the number of saplings that gro into a healthy and productive tree in the sample of 20 saplings

X~ Binomial ( 20, 0.7)

a) P(x=15) = 20C15 * (0.7)^15 * (1-0.7)^ 5

= 0.1789

b) P(x<15) = P( X ≤ 14) = 0.5836

c)  P(x>15) = 1- P( X ≤ 15) = 1- 0.7625 = 0.2375

d) P(x=16) = 20C16 * (0.7)^16 * (1-0.7)^ 4 = 0.1304

e) P(x≥16) = 1- P( X <16) = 1- P( X ≤ 15) = 1- 0.7625 = 0.2375

f) P(x≤16)= 0.8929