Answer:
Step-by-step explanation:
Number of sampled tyres = 10
To determine the mean, we will divide the total number of miles by the total number of tyres.
Mean, u = (42+36+46+43+41+35+43+45+40+39)/10 = 410/10 = 41
Standard deviation = √[summation(u - ub)^2]/n
ub = deviation from the mean, u
Summation(u - ub)^2] = (42-41)^2 + (36-41)^2 + (46-41)^2 +(43-41)^2 + (41-41)^2 + (35-41)^2 + (43-41)^2 + (45 -41)^2 + (40-41)^2 + (39-41)^2
= 1 + 25 + 25 + 4 + 0 + 36 + 4 + 16 + 1 + 4 = 116
Standard deviation = √116/10 = √11.6
= 3.41
We want to determine a 98% confidence interval for the mean mean lifetime of a particular brand of tire.
For a confidence level of 98%, the corresponding z value is 2.33. This is determined from the normal distribution table.
We will apply the formula
Confidence interval
= mean +/- z ×standard deviation/√n
It becomes
41 +/- 2.33 × 3.41/√10
= 41 +/- 2.33 × 10.78
= 41 +/- 25.11
The lower end of the confidence interval is 41 - 25.11 =15.89
The upper end of the confidence interval is 41 + 25.11 = 66.11
Therefore, with 98% confidence interval, the mean lifetime of a particular brand of tire is between 15.89 miles and 66.11 miles
