Question

Use the following information to determine your answer: The length of a movie falls on a normal distribution. About 95% of movies fall between 75 minutes and 163 minutes.
What is the value of the standard deviation for average movie length in minutes? Please round to the second decimal place.

Answer 1

Answer:

$75= 119 -1.96 \sigma$

$\sigma = \frac{75-119}{-1.96}= 22.45$

And tha's equivalent to use this formula:

$163= 119 +1.96 \sigma$

$\sigma = \frac{163-119}{1.96}= 22.45$

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:

$X \sim N( \mu, \sigma)$

We can estimate the true mean with the following formula:

$\mu = \frac{75+163}{2}= 119$

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:

$75= 119 -1.96 \sigma$

$\sigma = \frac{75-119}{-1.96}= 22.45$

And tha's equivalent to use this formula:

$163= 119 +1.96 \sigma$

$\sigma = \frac{163-119}{1.96}= 22.45$