Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution.
-The probability that a radish seed will germinate is 0.7. Estimate the probability that of 140 randomly selected seeds, exactly 100 will germinate.
A)0.0769
B)0.9331
C)0.0679
D)0.0669

Question

Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution.
-The probability that a radish seed will germinate is 0.7. Estimate the probability that of 140 randomly selected seeds, exactly 100 will germinate. 
A)0.0769
B)0.9331
C)0.0679
D)0.0669

Quizplus · Accepted Answer

To estimate the probability using the normal distribution as an approximation to the binomial distribution, we first find the mean (μ) and standard deviation (σ) of the binomial distribution. The mean μ = np and the standard deviation σ = sqrt(np(1-p)), where n is the number of trials (140) and p is the probability of success (0.7). Thus, μ = 140*0.7 = 98 and σ = sqrt(140*0.7*0.3) ≈ 6.2048. To find the probability of exactly 100 germinating, we convert this to a z-score and use the normal distribution. The z-score for 100 is (100-98)/6.2048 ≈ 0.322. Looking up this z-score in a standard normal distribution table or using a calculator gives a probability close to the value in option D, 0.0669, after accounting for continuity correction.

Estimate the Indicated Probability by Using the Normal Distribution as an Approximation