As reported by the US National Center for Health Statistics, the mean serum high-density-lipoprotein (HDL) ( 6pt) cholesterol of genetic females 20-29 years old is u = 53.0. The standard deviation is o = 12.0. Also, serum HDL cholesterol is normally distributed. (Statistics: Informed Decisions Using Data, Michael Sullivan, III) a. If one 20-29-year-old genetic female is randomly selected, what is the probability that their HDL cholesterol is between 45 and 55? b. If a hundred females, aged 20-29 years old, are randomly selected, what is the probability that the sample mean HDL cholesterol level is between 45 and 55? c. Fill in the following blank with number and explain how you can get that number. (Make sure to convert your answer into the unit of percentage with 3 digits after the decimal. For example, you can fill the number formatted as 12.345% into the blank) If we do a large number of sampling on the US population and each sample is of 10000 people, about % of sampling times would have the sample mean of HDL cholesterol level between 52.5 and 53.5