Burger King claims that their Whopper sandwich contains 580 calories. The calories in random sample of 8 Whoppers followed a normal model with a sample mean of 577.3 calories and a sample standard deviation of 41.32 calories.
Find the lower limit of a 95% confidence interval for the number of calories in a Whopper sandwich from Burger King. Round to three decimals.
To find the lower limit of the 95% confidence interval, we will use the formula:
Lower limit = sample mean - (critical value * (sample standard deviation / sqrt(sample size))
From the z-table, the critical z-value for a 95% confidence interval is 1.96.
Plugging in the values:
Lower limit = 577.3 - (1.96 * (41.32 / sqrt(8)))
Lower limit = 577.3 - (1.96 * (41.32 / 2.8284))
Lower limit = 577.3 - (1.96 * 14.617)
Lower limit = 577.3 - 28.6636
Lower limit = 548.636
Therefore, the lower limit of the 95% confidence interval for the number of calories in a Whopper sandwich from Burger King is 548.636 calories.