The mean life of a television set is 141
months with a variance of 256
.
If a sample of 71
televisions is randomly selected, what is the probability that the sample mean would be less than 136.3
months? Round your answer to four decimal places.
To calculate this probability, we first need to calculate the standard deviation of the sample mean. This is calculated using the formula:
Standard Deviation (σ) = sqrt(variance / sample size)
Standard Deviation (σ) = sqrt(256 / 71)
Standard Deviation (σ) = sqrt(3.6056)
Standard Deviation (σ) = 1.8976
Next, we calculate the z-score for the sample mean of 136.3 months:
z = (sample mean - population mean) / standard deviation
z = (136.3 - 141) / 1.8976
z = -2.4291
Now, we look up the z-score in the standard normal distribution table to find the probability:
P(z < -2.4291) = 0.0075
Therefore, the probability that the sample mean would be less than 136.3 months is 0.0075 (or 0.75%).