Question

The probability that a certain kind of flower seed will germinate is .80.

(a) If 194 seeds are planted, what is the probability that fewer than 141 will germinate? (Round standard deviation and your final answer to 4 decimal places.)

Probability()

(b) What is the probability that at least 141 will germinate? (Round standard deviation and your final answer to 4 decimal places.)

Probability ()

Answer 1

Solution:

Given that probability, = 0.80 and number of seeds planted, = 194

Since = 194 (0.80) = 155.2 and = 194 (1 - 0.80) = 38.8 both are greater than 5, we use normal approximation to binomial distribution.

Mean, = = 194 (0.80) = 155.2

Standard deviation, = = = 5.5714

a. Using continuity correction, X < 141 will be X < 140.5

The respective Z-score with X = 140.5 is

Z = -2.64

Now, we use Z-tables to find the probability Z less than -2.64

P (Z < -2.64) = 0.0041

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b. Using continuity correction, X 141 will be X > 140.5

The respective Z-score with X = 140.5 is

Z = -2.64

Now, we use Z-tables to find the probability Z greater than -2.64

P (Z > -2.64) = 1 - 0.0041 = 0.9959