Question

Suppose the speeds of vehicles traveling on a highway are normally distributed and have a known population standard deviation of 7 miles per hour and an unknown population mean. A random sample of 32 vehicles is taken and gives a sample mean of 64 miles per hour. Find the margin of error for the confidence interval for the population mean with a 98% confidence level.

Answer 1

Answer:

2.88

Step-by-step explanation:

Data provided in the question

$\sigma$ = Population standard deviation = 7 miles per hour

Random sample = n = 32 vehicles

Sample mean = $\bar X$ = 64 miles per hour

98% confidence level

Now based on the above information, the alpha is

= 1 - confidence level

= 1 - 0.98

= 0.02

For $\alpha_1_2$ = 0.01

$Z \alpha_1_2$ = 2.326

Now the margin of error is

$= Z \alpha_1_2 \times \frac{\sigma}{\sqrt{n}}$

$= 2.326 \times \frac{7}{\sqrt{32}}$

= 2.88

hence, the margin of error is 2.88