The actual tracking weight of a stereo cartridge that is set to track at 2.0 g on a particular changer can be regarded as a continuous rv X with the following pdf:. (x)={k[1−(x−3)^2] 2 ≤ x ≤ 4
0 otherwise
a. Find the value of k.
b. Sketch the graph of f(x).
c. What is the probability that the actual tracking weight is greater than the prescribed weigh?
d. What is the probability that the actual weight is within 0.25 g of the prescribed weight?
e. What is the probability that the actual weight differs from the presented weight by more than 0.5 g?

Atechnician compares repair costs for two types of microwave ovens (type i and type ii). he believes that the repair cost for type i ovens is greater than the repair cost for type ii ovens. a sample of 6767 type i ovens has a mean repair cost of $79.79$⁢79.79. the population standard deviation for the repair of type i ovens is known to be $19.18$⁢19.18. a sample of 5555 type ii ovens has a mean repair cost of $75.24$⁢75.24. the population standard deviation for the repair of type ii ovens is known to be $21.40$⁢21.40. conduct a hypothesis test of the technician's claim at the 0.050.05 level of significance. let μ1μ1 be the true mean repair cost for type i ovens and μ2μ2 be the true mean repair cost for type ii ovens. step 2 of 4 : compute the value of the test statistic. round your answer to two decimal places.