Normal distribution

Question

In a weightlifting championship that takes the form of a normal distribution with a mean of 265 and a standard deviation of 45, if an athlete wants to be in the top five of the distribution, what weight must he lift to achieve his desire?

Answer 1

You need to find the 90% confidence interval of the variable for weight,

say x=weight, convert x to a std normal variable 'z' , so you can create a 90% confidence interval for z.

The upper limit if that interval is the weight you need to achieve to be in the top 5% (recall the normal dis. is symmetric, so 5% of the data is beyond the upper limit of a 90% CI (confidence interval), and the bottom 5% is below the lower CI.

For this problem, your given the mean & std dev, so all you need to do is use the formula to convert the variable 'x' to a atd. normal:(x-265)/45. Next, look in the table to see what value of 'z' gives you. The bottom number of the CI gives you the numeric value to be above to be in the top 5% of the distribution.