Using diaries for many week, a study on the lifestyles of visually impaired students was conducted. The student kept track of many lifestyle variable including how many hours of sleep obtained on a typical day. Researchers found that visually impaired students averaged 9.2 hours of sleep with a standard deviation of 2.45 hours. Assume that the number of hours of sleep for these visually impaired students are normally distributed.
a) What is the probability that a visually impaired student gets at most 6.3 hours of sleep?
b) What is the probability that a impaired student gets between 6.9 and 8.59 hours of sleep?
c) What is the probability that a visually impaired student gets at least 7.3 hours of sleep?
d) What is the sleep time that cuts off the top 11.3% of sleep hours?
e) If 200 visually impaired students were studied, how many students would you expect to have sleep time of more than 8.59 hours?
f) A school district wants to give additional assistance to visually impaired students with sleep times at the first quartile and lower. What would be the maximum sleep time to be recommended for additional assistance?