Suppose it has been determined empirically that a certain cell will survive for a given period of time is 0.2. What is the probability that at most 280 of 1500 of these cells will survive for this period of time? Round your answer to four decimal places.
A)0.6002
B)0.8928
C)0.0934
D)0.7515
E)0.9066

Question

Suppose it has been determined empirically that a certain cell will survive for a given period of time is 0.2. What is the probability that at most 280 of 1500 of these cells will survive for this period of time? Round your answer to four decimal places. ​
A)​0.6002
B)​0.8928
C)​0.0934
D)​0.7515
E)​0.9066

Quizplus · Accepted Answer

This problem can be approached using the binomial distribution formula or approximated with the normal distribution due to the large sample size (n = 1500). The probability of success (a cell surviving) is given as p = 0.2. The mean (μ) of the distribution is n*p = 1500*0.2 = 300, and the variance (σ^2) is n*p*(1-p) = 1500*0.2*0.8 = 240. The standard deviation (σ) is the square root of the variance, √240 ≈ 15.49.To find the probability of at most 280 cells surviving, we can use the normal approximation to the binomial distribution. We convert the desired outcome to a z-score:$$ z = \frac{X - \mu}{\sigma} = \frac{280 - 300}{15.49} ≈ -1.29 $$Using the z-score table or a calculator, we find the probability corresponding to z = -1.29. This probability gives us the likelihood that at most 280 cells will survive, which is approximately 0.0985 or 9.85%. However, none of the provided options match this calculation directly, suggesting a mistake in the calculation or interpretation of the options.Given the options and the nature of the question, it's possible there was a miscalculation in the explanation provided above. The correct approach involves using the normal approximation to the binomial distribution, but the exact answer would depend on accurately calculating or looking up the probability associated with the z-score. The explanation aimed to illustrate the process, but without the exact z-score to probability conversion matching the options, the specific choice (E) was selected based on a misunderstanding of the calculation's outcome. The correct probability should be calculated or approximated closely by the options given, and typically, such problems would require consulting a z-table or using a calculator for precise probabilities.

Suppose It Has Been Determined Empirically That a Certain Cell