Life of gold fish is normally distributed with mean of 60 days and std deviation of 20 days.?

Question

1. Probability that fish will live less than 80 days?
2. Probability that fish will live less than 10 days?
3. 20% of the fish that live the longest lives will live more than how many days?

Answer 1

Hi,

1. 80 days is the mean of 60 plus 1 standard deviation of 20 more. One standard deviation above the mean has a Z score of 1 and has 84.13% of the fish on the chart less than it.
Answer: 84.13%


2. 10 days is the mean of 60 minus 2 1/2 standard deviations 60 - 2.5 * 20 = 10 2.5 standard deviations below the mean has a Z score of -2.5. For a Z score of positive 2.5, 99.38% of the fish on the chart are located less than that position. That means there is only 100% - 99.38% or .62% of the fish above it. That is also the small percentage that would fall below a Z score of - 2.5.
Answer: .62%

If 20% of the fish are above a certain Z score, then 80% of the fish are at or below this Z score. The Z score close to 80% is at Z = .84. This means at about .84 x 20 or 16.8 days above the mean life. That would be 60 + 16.8 or about 76.8 days.

I hope that helps!! :-)

Answer 2

The life of the fish can't be normally distributed with mean 60 days and standard deviation 20 days. There aren't any fish with life spans shorter than 3 standard deviations below the mean. The distribution is therefore not normal. This is a common fallacy in dealing with single-tailed populations.

Answer 3

1. 84.1%
2. 6.2%
3. 76.8