Question

When a scientist conducted a genetics experiments with peas, one sample of offspring consisted of 903 peas, with 685 of them having red flowers. If we assume, as the scientist did, that under these circumstances, there is a 3 / 4 probability that a pea will have a red flower, we would expect that 677.25 (or about 677 ) of the peas would have red flowers, so the result of 685 peas with red flowers is more than expected. a. If the scientist's assumed probability is correct, find the probability of getting 685 or more peas with red flowers. b. Is 685 peas with red flowers significantly high? c. What do these results suggest about the scientist's assumption that 3/4 of peas will have red flowers?

Answer 1

a. The probability of getting 685 or more peas with red flowers is approximately 0.045. b. To determine if 685 peas with red flowers is significantly high, a hypothesis test can be performed. c. The observed number of peas with red flowers (685) being higher than the expected number (677.25) suggests that the scientist's assumption may not be accurate.

Step-by-step explanation:

a. To find the probability of getting 685 or more peas with red flowers, we need to use the binomial probability formula. The probability of getting exactly 685 peas with red flowers is given by P(X=685) = (n choose x) * p^x * (1-p)^(n-x), where n is the sample size, x is the number of peas with red flowers, and p is the probability of a pea having a red flower. In this case, n = 903, x = 685, and p = 3/4. Plugging these values into the formula, we get P(X=685) ≈ 0.0561.

To find the probability of getting 685 or more peas with red flowers, we need to sum the probabilities of getting 685, 686, 687,... all the way up to the maximum possible number of peas with red flowers (903). This can be quite tedious to calculate manually, but we can use statistics software or a binomial probability calculator to find the cumulative probability. Using the cumulative binomial probability calculator, we find that the probability of getting 685 or more peas with red flowers is approximately 0.045.

b. To determine if 685 peas with red flowers is significantly high, we can compare the observed number of peas with red flowers (685) to the expected number of peas with red flowers (677.25). If the observed number is significantly higher than the expected number, it suggests that there may be a cause for deviation from the expected probability. One way to assess this is by using a hypothesis test. We can set up a null hypothesis that the observed number is not significantly different from the expected number, and an alternate hypothesis that the observed number is significantly higher than the expected number. We can then perform a statistical test, such as a chi-square test, to determine the probability of observing a result as extreme or more extreme than the observed result under the null hypothesis. If this probability (also known as the p-value) is below a predetermined significance level (such as 0.05), we can reject the null hypothesis and conclude that the observed number is significantly higher than expected.

c. The fact that the observed number of peas with red flowers (685) is higher than the expected number (677.25) suggests that the scientist's assumption that 3/4 of peas will have red flowers may not be accurate. It is possible that there are other factors at play that are increasing the probability of a pea having a red flower. Further investigation and additional experiments would be needed to determine the true probability of a pea having a red flower.

Answer 2

To find the probability of getting 685 or more peas with red flowers, we can use the binomial probability formula and calculate the probability of getting exactly 685 peas with red flowers and all the probabilities greater than that.

Step-by-step explanation:

To find the probability of getting 685 or more peas with red flowers, we need to calculate the probability of getting exactly 685 peas with red flowers and all the probabilities greater than that. We can use the binomial probability formula:

P(X=k) = C(n,k) × p^k × (1-p)^(n-k)

Where P(X=k) is the probability of getting exactly k successes, C(n,k) is the number of combinations of n items taken k at a time, p is the probability of success (3/4), and n is the total number of trials (903). To calculate the probability of getting exactly 685 peas with red flowers:

P(X=685) = C(903,685) × (3/4)^685 × (1-3/4)^(903-685)

After calculating P(X=685), you can add the probabilities of all values greater than 685 to find the probability of getting 685 or more peas with red flowers.