Question

A 99% confidence interval for the mean lifespan of Michellin ZX tires is 48500 miles to 56950 miles. Find the value of the sample mean and the margin of error.

Answer 1

Z_0.005=2.58

mean==a

T

Standard error==b

S n

CI=
T
+/- Z_0.005  
S n

CI=a +/- 2.58 *b

lower limit=48500

a-2.58 b=48500 ---------(1)

upper limit=56950

a+2.58 b=56950 -------------(2)

Adding 1 and 2 we get:

a+a=48500+56950

2a=105450

a=52725=mean(
T
)

putting this in 1:

52725 -2.58 b=48500

52725-48500=2.58 b

4225= 2.58 b

b=1637.5969=Standard Error(
S n
)

Hence, mean(
T
)=52725 and Standard Error(
S n
)=1637.6

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