The lengths of the eggs of a species of bird are roughly normally distributed, with a mean of 32 mm and an SD of 1.2 mm.
1.Approximately what is the 99th percentile of the lengths? Give your answer in mm but please do not enter the units.
2.Approximately 50% of the eggs have lengths in the range 32 mm plus or minus ____________ mm.
z = (x - 32)/1.2
For 1: you have to use a z-table to find the value where 99% of the values are less than that number meaning that there is 1% in the upper tail. Z-tables to differ from book to book, be sure to read it carefully.
Once you have that z- value, substitute it into the formula above and solve for x.
For #2, you are trying to find the values for the middle 50%. That means you will have 25% in each tail or .25.
Take that z-score and multiply it by the SD. This will give you that you would add or subtract from 32 mm.
26.46
it is not working , can u plz do it for me
To answer the first question, we need to find the value that corresponds to the 99th percentile of the normal distribution with a mean of 32 mm and a standard deviation of 1.2 mm.
1. To do this, we can use the Z-score formula: Z = (X - μ) / σ, where X is the value we want to find, μ is the mean, and σ is the standard deviation.
2. The 99th percentile corresponds to a Z-score of approximately 2.33. Using the formula above, we can rearrange it to solve for X:
X = Z * σ + μ
3. Plugging in the values, we get:
X = 2.33 * 1.2 + 32 = 34.796
Therefore, the 99th percentile length of the eggs is approximately 34.796 mm.
To answer the second question, we need to find the range within which 50% of the eggs' lengths fall.
1. Since the lengths of the eggs are normally distributed, we know that in a standard normal distribution, 50% of the data falls within 1 standard deviation of the mean.
2. Therefore, in our case, approximately 50% of the eggs have lengths in the range of 32 mm plus or minus 1.2 mm.
3. This means the range is:
32 mm - 1.2 mm to 32 mm + 1.2 mm, which simplifies to 30.8 mm to 33.2 mm.
Therefore, approximately 50% of the eggs have lengths in the range 32 mm plus or minus 1.2 mm.