Answer:
[tex] 75= 119 -1.96 \sigma[/tex]
[tex] \sigma = \frac{75-119}{-1.96}= 22.45[/tex]
And tha's equivalent to use this formula:
[tex] 163= 119 +1.96 \sigma[/tex]
[tex] \sigma = \frac{163-119}{1.96}= 22.45[/tex]
Step-by-step explanation:
For this case the 95%of the values are between the following two values:
(75 , 163)
And for this case we know that the variable of interest X "length of a movie" follows a normal distribution:
[tex] X \sim N( \mu, \sigma)[/tex]
We can estimate the true mean with the following formula:
[tex]\mu = \frac{75+163}{2}= 119[/tex]
Now we know that in the normal standard distribution we know that we have 95% of the values between 1.96 deviations from the mean. We can find the value of the deviation with this formula:
[tex] 75= 119 -1.96 \sigma[/tex]
[tex] \sigma = \frac{75-119}{-1.96}= 22.45[/tex]
And tha's equivalent to use this formula:
[tex] 163= 119 +1.96 \sigma[/tex]
[tex] \sigma = \frac{163-119}{1.96}= 22.45[/tex]
