Question

For the Devon Rex breed of cat; the number of kittens (X) born in single litter is approximated by the following probability distribution.

4%
9.7% 25.8% 34.2%
22.6%
6.3%
For a random sample of 10 Devon Rex cat litters, find the narrowest interval that would accurately predict the mean number of kittens per litter 95% of the time:

Answer 1

To predict the mean number of kittens per litter 95% of the time, a confidence interval should be constructed using the sample mean and standard deviation, along with a z-score for the 95% confidence level. However, we cannot determine the interval without further information.

Step-by-step explanation:

To find the narrowest interval that would accurately predict the mean number of kittens per litter 95% of the time for a random sample of 10 Devon Rex cat litters, we need to construct a confidence interval for the sample mean. The Central Limit Theorem allows us to assume that the distribution of the sample mean will be normally distributed because the sample size is sufficiently large. We would need additional information such as the mean number of kittens per litter and the standard deviation to calculate the exact interval. We also would utilize the appropriate z-score for the 95% confidence level to find the interval width. However, with the current information provided, we are unable to provide the narrowest interval.