Question

I don't mind you showing me the caluclator key strokes to do this

or show me the mathematical way whice ever thanks

Here is a simple probability model for multiple-choice tests. Suppose that a student has probability p of correclty ansering a question chosen at random form a univers of possible questions. (A strong student has a higher p than a weak student.) The correctness of an anser to any specific question doesn't depend on other quetions. a test contains n questions. Then the proportion of correct ansers that a student gives in a sample proportion p hat form an SRS of size n dranw from a population with population proportion p.

(a) Julie is a good student for whom p = .75. Find the probabilty that Julie socres 70% or lower on a 100-question test.

here what the back of the book says

P(p hat less than or equal to .50) = P(Z less than or equal to -1.155) = .1241