Westinghouse wants to determine the lifetime of its standard lightbulbs with an error 13 hours. Standard deviation is 120 hours. What sample size should they have to be 95% confident of the lifetime of their standard lightbulb?
a) 18.09 lightbulbs
b) 19 lightbulbs
c) 328 lightbulbs
d) 327.33 lightbulbs
Solution :
Given that,
standard deviation = = 120
margin of error = E = 13
At 95% confidence level the z is ,
= 1 - 95% = 1 - 0.95 = 0.05
/ 2 = 0.05 / 2 = 0.025
Z_{/2} = Z_{0.025} = 1.96
Sample size = n = ((Z_{/2} * ) / E)^{2}
= ((1.96 * 120) / 13)^{2}
= 327.33
Sample size = 327.33 lightbulbs
option D) is correct
Westinghouse wants to determine the lifetime of its standard lightbulbs with an error 13 hours. Standard...
A sample of size n=50 is taken from the production of lightbulbs at a certain factory. The sample mean of the lifetime of these 50 lightbulbs is found to be to X=1570 hours. Assume that the population standard deviation is a = 120 hours. (a) Construct a 95% confidence interval for . (b) What sample size is needed so that the length of the interval is 30 hours with 95% confidence?
Lightbulbs of a certain type are advertised as having an average lifetime of 750 hours. The price of these bulbs is very favorable, so a potential customer has decided to go ahead with a purchase arrangement unless it can be conclusively demonstrated that the true average lifetime is smaller than what is advertised. A random sample of 50 bulbs was selected, and the sample mean was found to be 738.44 with a standard deviation of 38.20 and a standard error...
Lightbulbs of a certain type are advertised as having an average lifetime of 750 hours. The price of these bulbs is very favorable, so a potential customer has decided to go ahead with a purchase arrangement unless it can be conclusively demonstrated that the true average lifetime is smaller than what is advertised. A random sample of 50 bulbs was selected, and the sample mean was found to be 738.44 with a standard deviation of 38.20 and a standard error...
Lightbulb lifetimes follow an unknown distribution, with a mean length of 10780 hours and a standard deviation of 370 hours. Suppose that a sample of 61 lightbulbs is taken. What is the probability that the total lifetime of these lightbulbs is less than 656193 hours? Select one: a. 1.0000 b. 0.4800 c. We cannot answer this question with the information given. d. 0.6844 e. 0.3156
the population standard deviation of the lifetime of washing machines is estimated to be 900 hours, how large a sample must be taken in order to be 90% confident that the margin of error will not exceed 100 hours? Select one: a. 219.18 b. 220 c. 14.8 d. 15
Lightbulb lifetimes follow an unknown distribution, with a mean length of 10702 hours and a standard deviation of 325 hours. Suppose that a sample of 72 lightbulbs is taken. What is the probability that the total lifetime of these lightbulbs is less than 768751 hours? Select one O a We cannot answer this question with the information given. O b.0.6500 c. 1.0000 od 0 7421 0.0.2579
If the population standard deviation of the lifetime of washing machines is estimated to be 900 hours, how large a sample must be taken in order to be 90% confident that the margin of error will not exceed 100 hours? Select one: a. 219.18 b. 220 c. 14.8 d. 15
Question 2 The average lifetime of a light bulb is 3,000 hours with a standard deviation of 696 hours A simple random sample of 36 bulbs is taken. a. What is the probability that the average life in the sample will be greater than 3,219 hours? What is the probability that the average life in the sample will be less than 3,180 hours? c. What is the probability that the average life in the sample will be between 2,670 and...
The average lifetime of a smoke detector is 5 years, or 60 months, and the standard deviation of lifetimes is 8 months. The lifetime of individual smoke detector units is a distribution that is right-skewed. A.) Using units of months, determine the sampling distribution of the sample mean for samples of size 200 smoke detectors. B.) Repeat part a. for sample size of 500. C.) Why can you still answer part a. and b. when the distribution of smoke detector...
QUESTION 15 A statistician employed by a consumer testing organization reports that at 95% confidence he has determined that the true average content of the Uncola soft drinks is between 12.714 to 13.286 ounces, but he forgot to report the size of the sample he had selected. Assuming the standard deviation of the population is 1.21, determine the size of the sample. (NOTE: ROUND YOUR ANSWER TO THE NEAREST INTEGER) QUESTION 16 If the population variance of the lifetime of...