solutions in detail and no software screenshot or shortcut p

solutions in detail, and no software screenshot or shortcut please...

Suppose that you simulate the elevator of a five story office building for 10 replications and obtain the following average delay in queue in each replication (in minutes): 135 17 5.40 308 1578 1339 145 147 137 43 3.26 3.78 3.08 5.78 5.19 4.46 4.73 3.71 4.37 a) b) c) Find the estimate for the average delay in queue. Construct a 90% CI for the average delay in queue Find the number of replications that is required to estimate the average delay in queue with an error of 0.4 minutes with 90% confidence.

Solution

a)
Average delay in queue = 4.376
b)
Confidence Interval
CI = x ± t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x)=4.376
Standard deviation( sd )=0.915
Sample Size(n)=10
Confidence Interval = [ 4.376 ± t a/2 ( 0.915/ Sqrt ( 10) ) ]
= [ 4.376 - 1.833 * (0.289) , 4.376 + 1.833 * (0.289) ]
= [ 3.846,4.906 ]
c)
Compute Sample Size
n = (Z a/2 * S.D / ME ) ^2
Z/2 at 0.1% LOS is = 1.64 ( From Standard Normal Table )
Standard Deviation ( S.D) = 0.915
ME =0.4
n = ( 1.64*0.915/0.4) ^2
= (1.501/0.4 ) ^2
= 14.074 ~ 15