Success Rates

Question

The following are success rates in % for math 11 over the past several semesters: 53.4, 47.7, 52.4, 55.1, 51.8, 46.9, 51.2, 54.2, 49.1, 55.5, 54.3, 61.9
the data listed shows the current grades for students in a sample of four of the math 11 classes is as follows , success is defined as a C grade or better
26 A’s , 35 B’s , 45 C’s , 22 D’s , 24 F’s
 

1.) using the sample data:
test the claim that the success rate in math 11 is greater than 60%. show all the steps in the hypothesis test,

2.) construct a 95% confidence interval of the proportion of successful students in math 11.

Question

The quality-control manager at a light bulb factory has determined the mean life of a light bulb is 755 hours with a standard deviation of 80 hrs

a)what percentage of light bulbs last between 770 and 790 hrs

b) how long would a light bulb have to last to be in the 98th percentile for longevity

c) what is the probability that a sample of 400 light bulbs would have a sample mean above 760?

d)What is the probability that a sample of 1600 light bulbs would have a sample mean above 760?