Question

You are a farmer whose farmland is cool, moist, and shady. (Assume that these growing conditions are equivalent to 80 drops/hr of water, 10% light, and a temperature of 13°C in the Gizmo.) You are thinking about planting seeds like Seed A in the Gizmo. You will turn a profit if at least 50% of your seeds become sprouts. Are you most likely to make money or lose money on this crop?

Answer 1

Define
n = number of seeds planted.
k = number of seeds that successfully become plants.

The probability of making a profit is
p =50% = 0.5
Therefore the probability of not makng a profit is
q = 1 - p = 0.5

According to the binomial distribution, the probability of k successes out of n trials is
$P(k \, of \, n) = _{n}C_{k}\,p^{k} q^{n-k} \\ where \\ _{n}C_{k} = \frac{n!}{k! (n-k)!}$

Create a table as shown below by using the graphing calculator.

  n      k   P(k of n)
----  -----  ------------
  4      2    0.375
  8      4    0.273
 10     5    0.246
  12    6    0.226
  16    8    0.196
  20  10    0.176
  50  25   0.0.112
 100  50   0.08

A graph of this table shows that the probability of success i below 0.5 (50%) for all practical values of n (the number of seeds planted).

Answer: The farmer will lose money.

Answer 2

Simple Answer:

A) Lose Money