The amount of time devoted to studying statistics each week by students who achi

Question

The amount of time devoted to studying statistics each week by students who achieve a grade A in the course is normally distributed random variable with a mean of 7.5 hours and a standard deviation of 2.1 hours. a) What proportion of these students study for more than 10 hours? b) Find the probability that such a student spends between 7 and 9 hours studying. c) What proportion of these students spend less than 3 hours studying? d) What is the amount of time below which 5%of all the students spend Studying?

Explanation / Answer

mean = 7.5 , std, deviation = 2.1

a) P(x>10)

z = ( x - mean) / s

= ( 10 - 7.5) / 2.1

= 1.190

we need to find P(Z>1.190)

p(X>10) = P(z>1.190) = 0.1169

b) P(7 < X < 9)

z = ( x - mean) / s

= ( 7 - 7.5) / 2.1

= -0.238

P(X < 9)

z = ( x - mean) / s

= ( 9 - 7.5) / 2.1

= 0.714

P(7<X<9) = P(-0.238<z< 0.714) = 0.3566

c)

P(X<3)

z = ( x - mean) / s

= ( 3 - 7.5) / 2.1

= -2.14

we need to find P(Z<-2.14)

p(X<3) = P(z < -2.14) = 0.0161

d) z value at 5% = -1.645

x bar = mean +z*s

= 7.5 -1.645 * 2.1

= 4.0455

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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