Mendelian Genetics When Mendel conducted his famous genetics e...

Question

Mendelian Genetics When Mendel conducted his famous genetics experiments with peas, one sample of offspring consisted of 929 peas, with 705 of them having red flowers. If we assume, as Mendel did, that under these circumstances, there is a 3/4 probability that a pea will have a red flower, we would expect that 696.75 (or about 697) of the peas would have red flowers, so the result of 705 peas with red flowers is more than expected.

a. If Mendel’s assumed probability is correct, find the probability of getting 705 or more peas with red flowers.

a. If Mendel’s assumed probability is correct, find the probability of getting 705 or more peas with red flowers.

Accepted Answer

All right, hello everyone. So this question says, during a genetic experiment with a certain type of bacteria, a scientist observes that there is an 80% chance of a bacteria colony exhibiting a specific resistance trait. Out of 500 colonies, 420 show the resistance trait. If the scientist's assumption is correct, find the probability of observing 420 or more colonies with the resistance trait. Option A says 0.0184, B says 0.0275, C says 0.0146, and option D says 0.0125. So, recall that in order to find the probability of observing 420 or more colonies with this trait, we're going to have to find the the score that's relevant for this question. So first we have to begin with finding the mean and the standard deviation. So the mean or mu. Is equal to NP. So N in this case is the total number of colonies observed, and P is the probability of any colony exhibiting that resistance trait. So plugging in the information obtained from the text of the question, N is equal to 500. And P is equal to 80% or 0.80. Multiplying these two numbers together gives you mu, which once again is the mean of 400. So from here you can identify or you can calculate rather the standard deviation, sigma. Sigma. is equal to the square root of NP multiplied by one subtracted by P. So once again plugging in the information we obtained beforehand, that's the square root of 500 multiplied by 0.80. And then multiplied by 1 subtracted by 0.80. Evaluating this expression gives you a standard deviation equal to 8.944. So now we want to apply the continuity correction. Because here, in this case, what we're solving for is the probability of X, which represents the number of colonies, being greater than or equal to 420. So when we apply the continuity correction. That turns out to be. The probability of X being greater than or equal to 419.5. So now, when calculating the D score. X would be equal to 419.5. Recall that Z is equal to X subtracted by mu divided by sigma. So X is 419.5. Subtracted by 400. And then that difference is divided by 8.944. Evaluating this expression gives you a Z score of 2.18. And so now that you've obtained the Z score itself, you would find the probability corresponding to that particular table, or that particular Z score, using the standard normal curved table. So after referencing the standard normal curve, The probability of a Z score equal to 2.18. Is approximately 0.9854. And now we are, we've arrived at the final step of the calculation, because using the probability that we just found, Subtracting this by one gives you the probability. Of Z being greater than or equal to. 2.18 So once again, one subtracted by 0 point. 9854. Equals 0.0146. And that corresponds to option C in the multiple choice. And there you have it. So with that being said, thank you so very much for watching, and I hope you found this helpful.

Key Concepts

Probability Distribution

Binomial Probability Formula

Normal Approximation to the Binomial

Watch next