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

Answer:

Check the explanation

Step-by-step explanation:

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

or , $P\left (\frac{(n-1)s^2}{\sigma^2}<(n-1)p \right )=0.05$

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

or , 5p =1.145476

or , $p =\frac{1.145476}{5}= 0.2290952$

Required percentage = 22.91