The mean time of the entire operation is given by 31 seconds and standard deviation is approximately 4.47 seconds
mean time (μ₁) = 11 seconds
mean chassis time (μ₂) = 20 seconds
a)Total time taken = μ₁ + μ₂ = 11 +20 = 31 seconds
Now we will find the standard deviation:
standard deviation = √ (2²+4²) = √ 20 ≈ 4.47 seconds
b) The probability that the entire process will take less time:
Total time taken = 31 seconds
Less time taken will be 2 seconds for the entire time
P(T<30) = 30 - 31 / 4.47 = - 0.22
Now from the normal distribution table we get the p-value as :
p-value = 0.4129
Hence the required probability is 41.29 % .
The population or sample standard deviation and the standard error of a statistic are not the same thing, but they are related. The standard error of the sample mean is the standard deviation of the set of means computed by drawing an infinite number of repeated samples from the population and computing a mean for each sample.
The mean's standard error is estimated by dividing the sample standard deviation by the square root of the sample size, which matches the population standard deviation divided by the square root of the sample size.
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