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

Question

Question 5 (2 points) d 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 0.748 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 all entering freshmen planned to major in a STEM (science, technology, engineering, mathematics) discipline. A sample of 36 freshmen is selected. What is the probability that the proportion of freshmen in the sample is between 0.490 and 0.580? Write only a number as your answer Round to 4 decimal places (for example 0.3748). Do not write as a percentage. Your Answer

Explanation / Answer

5)
p= 0.74
n= 81

E(phat) = p = 0.74
V(Phat) = pq/n = 0.74*(1-0.74)/81 = 0.0024
SD(phat) = sqrt(V(phat)) = SQRT(0.0024) = 0.048989795

P( X>0.748)
= 1 - P(X<0.748)

I know that, z = (X-mean)/(sd)
z1 = (0.748-0.74)/0.049)
z1= 0.1633

hence,
P( X>0.748)
=1- P(Z<0.1633)
1 - NORMSDIST(0.1633)
0.4351

6)
p= 0.5
n= 36

E(phat) = p = 0.5
V(Phat) = pq/n 0.5*(1-0.5)/36 0.0069
SD(phat) = sqrt(V(phat)) SQRT(0.0069) 0.0831

P(0.49 < X < 0.58)
= P(X<0.58) - P(X<0.49)

I know that, z = (X-mean)/(sd)
z1 = (0.49-0.5)/0.0831)
z1= -0.1203
z2 = (0.58-0.5)/0.0831)
z2= 0.9627

hence,
P(0.49 < X < 0.58)=
= P(Z<0.9627) - P(Z<-0.1203)
= NORMSDIST(0.9627) - NORMSDIST(-0.1203)
0.3800

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.