A random sample of truck speeds for 15 randomly selected trucks traveling on Route 95 in New Rochelle was taken. These a

[answerhappygod]

A random sample of truck speeds for 15 randomly selected truckstraveling on Route 95 in New Rochelle was taken. These are theresults (in miles per hour):57.3, 65.5, 51.3, 66.1, 74.8, 68.9, 63.9, 62.4, 56.4, 57.9, 55.2,57.2, 59.9, 66.9, 58.4Truck speeds on Route 95 are known to be normally distributed withan unknown mean of 𝜇 and an unknown standarddeviation 𝜎. (in miles per hour)Calculate the sample mean for this data. b) Calculate the sample standard deviation for thisdata. c) Calculate the maximum likelihood estimatefor 𝜎2 using this data. d) Calculate an unbiased estimate for 𝜎2 usingthis data. e) Calculate the sample median for this data. f) Suppose W has a t distribution with 14 degrees of freedom. IfP(W > t) = .09 then what is t? g) Suppose W has a t distribution with 14 degrees of freedom. IfP(W < t) = .09 then what is t? h) Calculate the 91st percentile of a standard normaldistribution. i) Compute an 82% confidence interval for 𝜇 using youranswers above. ( _____ , _____)
j) Compute an 82% prediction interval for 𝜇 using youranswers above. ( _____ , _____ )
k) Copy your R script or other comments for the above into thetext box here.