A financial services company is looking to study the types of investments participants make within their online platform. It is known that 56% of the population allocates a quarter of their investments in real estate. If the financial service company randomly samples 45 participants, use a calculator to find the probability that more than half of them have a quarter of their investments in real estate. Round your answer to three decimal places.

Evaluate the expression for the given value of the variable 2×(c2-5) for c=4

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.

In the next 10 years, how do you think hipaa guidelines will affect the roles, responsibilities and tools of a medical transcriptionist