Answer to Question #154685 in Statistics and Probability for Shawnitra Jackson

Question

The manufacture of fertilizer guarantees that, with the aid of the fertilizer, 75% of planted seeds will germinate. Suppose the manufacturer is correct. If 7 seeds planted with the fertilizer are randomly selected, what is the probability that more than 5 of them germinate? Carry your intermediate computations to the least four decimal places, and round your answer to two decimal places.

Answer 1

We are to determine the probability that more than 5 of 7 seeds (i.e. 6 or 7) germinate.

The probability that all 7 seeds germinate is equal 0.75⁷= 0.133484 = 13.3484%.

The probability that only the first (only the second, etc) seed does not germinate is equal 0.25 * 0.75⁶= 0.044495 = 4.4495%.

The probability that 6 seeds germinate is the sum of the probabilities that only the first seed does not germinate, only the second one does not germinate, etc, and equals to 7 * 0.044495 = 0.311465 = 31.1465%.

The total probability that more than 5 of 7 seeds germinate is the sum of the probabilities that 7 seeds germinate and that 6 seeds germinate, i.e. 13.3484% + 31.1465% = 44.4949%.