Question

A random sample of 10 chocolate energy bars of a certain brand has, on average, 230 calories per bar, with a standard deviation of 15 calories. Construct a 99% confidence interval for the true mean calorie content of this brand of energy bar. Assume that the distribution of the calorie content is approximately normal.

Answer 1

214.389 to 245.611 calories

Explanation:

A confidence interval can be constructed as follows:

Lower bound (L):

`L = X - Z(s)/(√(n))`

Upper bound (U):

`U = X + Z(s)/(√(n))`

Where 'X' is the sample mean, 's' is the sample standard deviation, 'n' is the sample size, and Z is the x-score associated with the confidence interval.

In this problem

X = 230; S= 15; n=10; and for a 99% confidence interval, z = 3.291

The upper and lower bounds are:

`L = 230 - 3.291(15)/(√(10))\\L= 214.389\\U = 230 + 3.291(15)/(√(10))\\U= 245.611`

The confidence interval is 214.389 to 245.611 calories.