Question

The number of eggs that a female house fly lays during her lifetime is normally distributed with mean 760 and standard deviation 110. Random samples of size 100 are drawn from this population, and the mean of each sample is determined. What is the probability that the mean number of eggs laid would differ from 760 by less than 20? Round your answer to four decimal places.

Answer 1

Given that,

The number of eggs that a female house fly lays during her lifetime is normally distributed with mean 760 and standard deviation 110. Sample size (n) = 100

To find, the probability that the mean number of eggs laid would differ from 760 by less than 20. That is to find,

  

  

  

Therefore, the probability that the mean number of eggs laid would differ from 760 by less than 20 is 0.0344

Note:

1) Using standard normal z table we get P(Z <= 1.82) = 0.9656

2) If you want then it is zero ( ) because in normal dustribution exact probability is zero.