12. Face masks used by firefighters often fail by having their lenses fall out when exposed to very high temperatures. A manufacturer of face masks claims that for its masks the average temperature at which pop-out occurs is 550 F. A sample of 75 masks is tested, and the average temperature at which the lenses popped out was 470 F. Suppose an estimate of o is 0.7 a. If the level of confidence remains 99% but the desired width of the interval is reduced to 0.3, what is the necessary sample size? b. If the level of confidence is reduced to 95% but the desired width of the interval remains 0.5, what is the necessary sample size? Homework # 2 Biostatistics CLS 603 c. Describe the impact on the value of the sample size of increases (decreases) in the level of confidence for a fixed desired width. d. Describe the impact on the value of the sample size of increase (decreases) in the desired width for a fixed level of confidence. 13. Suppose the students' mathematics scores conform to a normal distribution with # = 75,0 =10. a. What proportion of students will have scores higher than 94.6? b. What proportion of students will have scores between 49.2 and 100.8? c. What score will be exceeded by 10% of the students? d. Suppose a random sample of n = 64 test scores is selected; what is the standard error of the sampling distribution