any state auto insurance company took a random sample of 370 insurance claims paid out during a 1-year period. the average claim was $750 with a standard deviation of $150. find .99 confidence interval for the mean claim payment.
Formula:
CI99 = mean ± (z-value)(sd/√n)
mean = 750
sd = 150
n = 370
Find the z-value using a z-table for 99% confidence, then calculate your interval.
I hope this will help get you started.
To find the 99% confidence interval for the mean claim payment, we can use the formula:
CI = X̄ ± Z * (σ/√n)
Where:
CI = Confidence Interval
X̄ = Sample mean
Z = Z-score for the desired confidence level
σ = Population standard deviation
n = Sample size
In this case, the sample mean (X̄) is $750, the standard deviation (σ) is $150, and the sample size (n) is 370.
Step 1: Determine the Z-score
To find the Z-score for a 99% confidence level, we need to find the corresponding value from the Z-table or use a statistical software. The Z-score for a 99% confidence level is approximately 2.57.
Step 2: Calculate the margin of error
The margin of error is given by Z * (σ/√n). Plugging in the given values, we have:
Margin of error = 2.57 * (150/√370)
Step 3: Calculate the confidence interval
The confidence interval is calculated by adding and subtracting the margin of error from the sample mean (X̄). Therefore,
CI = $750 ± Margin of error
Now, let's calculate the margin of error and the confidence interval:
Margin of error = 2.57 * (150/√370)
CI = $750 ± Margin of error
After calculating the margin of error and substituting it into the confidence interval formula, we can find the 99% confidence interval for the mean claim payment.