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%).
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.
1 answer