Question

A production process manufactures electronic components with timing signals whose duration follows a normal distribution. A random sample of 55 components was​ taken, and the durations of their timing signals were measured.a. The probability is 0.01 that the sample variance is bigger than what percentage of the population​ variance?

b. The probability is 0.05 that the sample variance is less than what percentage of the population​ variance?

Answer 1

Check the explanation

Explanation:

b )
`P(s^2<p\sigma^2)=0.05`

or ,
`P\left (((n-1)s^2)/(\sigma^2)<(n-1)p \right )=0.05`

or ,
`P\left (\chi^2_5<5p \right )=0.05=P(\chi^2_5< 1.145476 )`

or , 5p =1.145476

or ,
`p =(1.145476)/(5)= 0.2290952`

Required percentage = 22.91