An exhaustive study of all active Facebook accounts was recently conducted by Facebook. One variable Facebook recorded was the number of friendsXof each Facebook user. SupposeXhas expected value E(X) =182and standard deviation SD(X) =293.3. Since the possible values ofXare only integers and since the distribution ofXis highly skewed to the right, the distribution ofXcannotbe described by a normal model. Suppose you select a random sample of30Facebook users and record the number of Facebook friends each user has.

1. What is the probability that the 30 Facebook users in your sample have a sample mean number of friends x greater than 184?

2. What is the probability that the 30 Facebook users in your sample have a sample mean number of friends x less than 215?

One of the methods forensic investigators use for estimating the age at death of a human, or the age of a living individual (for example for legal reasons or to verify identity) is based on measurement of the biochemical changes in amino acids within the teeth or bones. As bones and teeth age the ratio (R/L) of two amino acids, denoted simply as R and L, increases. The biochemical changes that occur over time in these amino acids follow an exponential law. The age t, in years, can be estimated from (R/L) using the equation t = b0 + b1*LN((1+R/L)/(1-R/L))^(), where LN denotes the natural logarithm (logarithm base e).

This Excel file has data on the ratio (R/L) from the teeth of human subjects of known age.

intercept: -26.72

slope: 808.65

Age of death:46.1

Calculate a 95% prediction interval for the age at death of Sherlock Holmes' surprise garden visitor.

lower bound:

higher bound: