Question

60% of a certain species of tomato live after transplanting from pot to garden. Eli transplants 16 of these tomato plants in a garden each month. Assume that the plants live independently of each other. Let X equals the number of tomato plants that live each month.

Find

1) the mean of X. (Give your answer to 1 decimal place.)

2) the standard deviation of X. (Give your answer to 2 decimal places.)

Answer 1

This is a binomial distribution since we have two possible outcome, fixed success rate and independence of each observations .

n=16

p=0.6

mean=np

mean=$16\cdot0.6$

mean=9.6

standard deviation =$\sqrt{n\cdot p \cdot(1-p)}$

standard deviation =$\sqrt{16\cdot0.6\cdot(1-0.6}$

standard deviation =1.96