Question

In an certain species of newt, offspring are born either green or black. Suppose that 40% of these newts are born green. If we sample 121 of these newts at random, the probability distribution for the proportion of green newts in the sample can be modeled by the normal distibution pictured below. Complete the boxes accurate to two decimal places . Note: The left box is 2 standard deviations below the mean. The middle box is the mean.

Answer 1

To model the probability distribution for the proportion of green newts in the sample, we can use the normal distribution. The mean of the distribution is 0.40 and the standard deviation is approximately 0.0486. The shaded area in the graph represents the probability that the proportion of green newts in a sample is less than a certain value.

Step-by-step explanation:

The question is asking about the probability distribution for the proportion of green newts in a sample. In this case, 40% of the newts are born green. To model this probability distribution, we can use the normal distribution. The mean of the distribution is equal to the proportion of green newts, which is 0.40. The standard deviation can be calculated as the square root of (0.40 * (1 - 0.40) / 121), which is approximately 0.0486.

The shaded area in the graph represents the probability that the proportion of green newts in a sample is less than the given value of x. To find the values for the boxes in the graph, we can use a standard normal distribution table or a calculator. The left box represents 2 standard deviations below the mean, which is approximately 0.40 - (2 * 0.0486) = 0.3028. The middle box represents the mean, which is 0.40. The right box represents 2 standard deviations above the mean, which is approximately 0.40 + (2 * 0.0486) = 0.4972.