ing. time value is such that the total lifetime of all batteries in the a package exceeds that value for only 5% of all packages? e is n is 53. Rockwell hardness of pins of a certain type is known to...

I am focused on question 54 here. Thanks for your understanding and solutions.

Extracted text: ing. time value is such that the total lifetime of all batteries in the a package exceeds that value for only 5% of all packages? e is n is 53. Rockwell hardness of pins of a certain type is known to have a mean value of 50 and a standard deviation of 1.2. a. If the distribution is normal, what is the probability that the sample mean hardness for a random sample of 9 pins is at least 51? b. Without assuming population normality, what is the (approximate) probability that the sample mean hardness for a random sample of 40 pins is at least 51? 277 size pu- the ean la- lue 54. Suppose the sediment density (g/cm) of a randomly selected specimen from a certain region is normally distrib- uted with mean 2.65 and standard deviation .85 (suggested in "Modeling Sediment and Water Column Interactions for Hydrophobic Pollutants," Water Research, 1984: 1169–1174). ass. Dws irst cted a. If a random sample of 25 specimens is selected, what is the probability that the sample average sediment density is at most 3.00? Between 2.65 and 3.00? b. How large a sample size would be required to ensure that the first probability in part (a) is at least .99? ctor asly, e is ews 55. The number of parking tickets issued in a certain city on any given weekday has a Poisson distribution with rob- vaits parameter u 50. a. Calculate the approximate probability that between 35 and 70 tickets are given out on a particular day. b. Calculate the approximate probability that the total number of tickets given out during a 5-day week is between 225 and 275. c. Use software to obtain the exact probabilities in (a) and (b) and compare to their approximations. cted n the nean X is Stay dent orpa 56. A binary communication channel transmits a sequence of "bits" (0s and 1s). Suppose that for any particular bit