The length of a movie falls on a normal distribution. About 95% of movies fall between 75 minutes and 163 minutes. Required:

a. What is the mean value for average movie length in minutes?

b. What is the value of the standard deviation for average movie length in minutes?

a) x = 119 minutes

the mean value for average movie length in minutes is 119 minutes

b) margin of error M.E = 44 minutes

Note; Since the number of samples used is not given, the standard deviation r cannot be calculated using the equation

M.E = zr/√n

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

x+/-M.E

M.E = zr/√n

Given that;

M.E = margin of error

Mean = x

Standard deviation = r

Number of samples = n

Confidence interval = 95%

z value (at 95% confidence) = 1.96

a) The mean value x can be calculated as;

x = (a+b)/2

Where a and b are the lower and upper bounds of the confidence interval;

a = 75 minutes

b = 163 minutes

substituting the values;

x = (75+163)/2

x = 119 minutes

the mean value for average movie length in minutes is 119 minutes

b) the margin of error M.E can be calculated as;

M.E = (b-a)/2

Substituting the values;

M.E = (163-75)/2

M.E = 44 minutes

Since the number of samples used is not given, the standard deviation r cannot be calculated using the equation

M.E = zr/√n

step-by-step explanation:

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