To ensure that 95% of bulbs do not fall short on the guaranteed average by more than 2%, we need to calculate the margin of error.
Margin of error = 2% of 1500 hrs = 0.02 * 1500 = 30 hrs
We want to be 95% confident that the true average life of the bulbs will be within 30 hrs of the guaranteed average. Since the sample standard deviation is known, we can use the formula for calculating the sample size for a given margin of error:
n = (Z * SD / E)^2
Where:
n = sample size
Z = Z-score corresponding to the desired level of confidence (95% in this case, which corresponds to a Z-score of 1.96)
SD = standard deviation of the population (120 hrs)
E = margin of error (30 hrs)
Substitute the values into the formula:
n = (1.96 * 120 / 30)^2
n = (235.2 / 30)^2
n = 7.84^2
n = 61.50
Therefore, the minimum sample size needed to ensure that 95% of bulbs do not fall short on the guaranteed average by more than 2% is 62.
The guaranteed average life of a certain type of electric bulbs is 1500 hrs with a S.D. of 120 hrs. It is decided to sample the output so as ensure that 95% of bulbs do not fall short on the guaranteed average by more than 2%. What will be the minimum sample size?
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