The mean incubation time of fertilized eggs is 23 days. Suppose the incubation times are approximately normally distributed with a standard deviation of 1 day. (a) Determine the 17th percentile for incubation times. (b) Determine the incubation times that make up the middle 97 %.

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Mathematics

18 January, 01:20

The mean incubation time of fertilized eggs is 23 days. Suppose the incubation times are approximately normally distributed with a standard deviation of 1 day. (a) Determine the 17th percentile for incubation times. (b) Determine the incubation times that make up the middle 97 %.

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Aspen Landry · Answer 1

a) The 17th percentile would be 22 days

b) 97% of the values will fall within 21 and 25 days

Step-by-step explanation:

To find the first part of this question you need to know the basic normal distribution curve. The 17th percentile falls roughly at - 1 standard deviations from the mean. Given that the mean is at 23 days, we know the 17th percentile would be at 22 days.

In order to solve part b, know that the normal distribution curve shows 97% of the values within - 2 and + 2 standard deviations away from the mean. This gives us values of 21 and 25 days.