Question 1.05 It is known from past experience that the life of traffic light bulbs is normally distributed with a standard deviation of 250 hours. In a study, if you wanted the total width of the two-sided confidence interval on mean to be 120 hours at 90% confidence, how many light bulbs should be selected for the study

The required sample size of lightbulbs = 47

Step-by-step explanation:

The total width of the two-sided confidence interval on mean to be 120 hours at 90% confidence.

That is, 60 hours on top and below the mean.

Confidence interval = (Sample mean) ± (Margin of error)

So, from this description that the interval is of width 120 hours of the mean and 60 hours, below and above the mean,

Margin of error = 60 hours.

Margin of Error = (critical value) × (standard deviation of the distribution of sample means)

Critical value for 90% confidence = 1.645

Standard deviation of the distribution of sample means = (standard deviation) ÷ √n

where n = sample size = ?

Standard deviation = 250 hours

60 = 1.645 × (250/√n)

√n = (1.645×250)/60 = 6.854

n = 6.854² = 46.98 = 47 (approximated to the closest whole number)

Hope this Helps!!!

So the answer for this case would be n=47 rounded up to the nearest integer

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

represent the sample mean for the sample  

population mean (variable of interest)

represent the population standard deviation

n represent the sample size  

Solution to the problem

For this case the width of the interval is 120 and we have the following relation:

The margin of error is given by this formula:

   (a)

And on this case we have that ME =60 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

  (b)

The critical value for 90% of confidence interval now can be founded using the normal distribution. And in excel we can use this formula to find it:"=-NORM.INV(0.05;0;1)", and we got , replacing into formula (b) we got:

So the answer for this case would be n=47 rounded up to the nearest integer

146%

step-by-step explanation: