Question

The life in hours of a 75-watt light bulb is known to be normally distributed with σ = 22 hours. a random sample of 20 bulbs has a mean life of x overscript bar endscripts = 1012 hours. suppose that we wanted the total width of the two-sided confidence interval on mean life to be six hours at 95% confidence. what sample size should be used? round up the answer to the nearest integer.

Answer 1

Answer:

207

Step-by-step explanation:

Data provided in the question:

σ = 22 hours

Mean = 1012 hours

Confidence level = 95%

Width of the confidence level = 6 hours

Therefore,

Margin of error, E = ( Width of the confidence level ) ÷ 2

= 6 ÷ 2

= 3

also,

E = $z\times\frac{\sigma}{\sqrt n}$

here,

z value for 95% confidence level  is 1.96

Thus,

3 = $1.96\times\frac{22}{\sqrt n}$

or

√n = $1.96\times\frac{22}{3}$

or

√n = 14.373

or

n = 206.59 ≈ 207