Question 5 (2 points) 74% of freshmen entering public high schools in 2006 gradu

Question

Question 5 (2 points) 74% of freshmen entering public high schools in 2006 graduated with their class in 2010, A random sample of 81 freshmen is selected. Find the probability that the proportion of students who graduated is greater than 0.749. Write only a number as your answer. Round to 4 decimal places (for example 0.1048). Do not write as a percentage. Your Answer: Answer Save Question 6 (2 points) At a certain university, 50% of entering freshmen planned to major in a STEM (science, technology, engineering. mathematics) disipine. A cample of 36 freshmen is selected. What is the probability that the proportion of freshmen in the sample is between 0479 and 0 580 Wrte only s number as your anever, Round to 4 decimal places (for example 0:3748) Do not write as a percentage

Explanation / Answer

Q5.

the PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd/sqrt(n) ~ N(0,1)
proportion ( p ) = 0.74
standard Deviation ( sd )= sqrt(PQ/n) = sqrt(0.74*0.26/81)
=0.0487
P(X > 0.749) = (0.749-0.74)/0.0487
= 0.009/0.0487 = 0.1848
= P ( Z >0.185) From Standard Normal Table
= 0.4267

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