The Questions are of STATISTICS FOR MACHINE LEARNING:

1) A premium cricket bat production company must produce all of its bats to 1.25kg. Samples are drawn hourly and checked. If the production line gets out of sync with a statistical significance of more than 5%, it must be shut down and bat manufacturing machine needs to be repaired.This hour's sample of 15 bats are produced and weights of the bat are given below. Conduct the statistical analysis to check whether the shut down of production is required. Assume that data is normally distributed.

bat_weight =[1.32,1.57,1.49,1.22,1.26,1.31,1.17,1.5,1.62,1.28,1.36,1.39,1.44,1.25,1.54]

i) Create the Hypothesis.

ii) Determine the Statistical Test and give the reason for selection of the test.

iii) Manual Calculation of test statistics and pvalue.

iv) Use the inbuilt function. Prove the results of inbuilt function and manual calculation are equal.

v) Interpret the Results.

2) There are totally 100 boats in a port.If on an average 2 ship out of 10 do not arrive safely to ports.

i) Probability of getting exactly 12 boats to sink

ii) Probability of getting atleast 12 boats to sink

iii) Probability of getting atmost 12 boats to sink

iv) Probability of getting between 10 and 15 boats to sink