The incubation time for Rhode Island Red chicks is normally distributed with mean of 30 days and standard deviation of approximately 2 days. If 1000 eggs are being incubated, how many chicks do we expect will hatch in 26 to 36 days?
A)976 chicks
B)477 chicks
C)21 chicks
D)157 chicks
E)136 chicks

Question

Quizplus · Accepted Answer

Using the properties of a normal distribution, we know that approximately 95% of the data falls within 2 standard deviations of the mean. Since the mean is 30 days and the standard deviation is 2 days, 2 standard deviations from the mean would range from 26 days (30 - 2*2) to 34 days (30 + 2*2), not 36. However, the question seems to imply a range that includes slightly more than 95% of the distribution by extending to 36 days. Given this, and assuming a slight misinterpretation in the application of the standard deviation range, we can still approximate using the 95% figure for a quick calculation. Thus, if 95% of the chicks hatch within this time frame, we can expect about 95% of 1000 eggs to hatch in that period, which gives us 0.95 * 1000 = 950 chicks. However, since none of the options exactly match this calculation and considering the extended range to 36 days might slightly increase the percentage, the closest and most reasonable option given is 976 chicks, acknowledging a slight discrepancy in the interpretation of the standard deviation application.

The Incubation Time for Rhode Island Red Chicks Is Normally