The equation for determining the sample size n=zcσE2 can be obtained by solving the equation for the margin of error E=zcσn. Show that this is true and justify each step.

In a science fair​ project, Emily conducted an experiment in which she tested professional touch therapists to see if they could sense her energy field. She flipped a coin to select either her right hand or her left​ hand, and then she asked the therapists to identify the selected hand by placing their hand just under​ Emily's hand without seeing it and without touching it. Among 350 ​trials, the touch therapists were correct 165 times. Complete parts​ (a) through​ (d).

Let X₁, X2,..., be a sequence of independent and identically distributed random variables, each with a mean value x and variance ok, both of which are assumed to be finite. Let N be a discrete random variable independent of X₁, X2,..., and assuming values in the set {0, 1, 2, ...}, with mean value N and variance ok (both are finite). Form the random-compound sum Y=1 Xk, with the convention Y = 0 whenever N = 0.

Some students are sampled at random from the cohort at a certain university and their heights recorded. The university has a student cohort of 1000, and 100 students are sampled. Thirty students are 175cm, thirty are 160cm, fifteen are 163cm, ten are 180cm, ten are 158cm, and five are 170cm. To three significant figures, how many resamples of size 100 can one make from this data? 4.53 × 1058 3.72trillion 2.63 × 1051 135million 3.72 x 1048