(1 point) Using diaries for many weeks, a study on the lifestyles of visually im

Question

(1 point) Using diaries for many weeks, a study on the lifestyles of visually impaired students was conducted. The students kept track of many lifestyle variables including the number x of hours of sleep obtained on a typical day. Researchers found that visually impaired students averaged 9.92 hours of sleep, with a standard deviation of 1.75 hours. Assume that the number of hours of sleep for these visually impaired students is normally distributed (a) What is the probability that a visually impaired student gets less than 6.4 hours of sleep? P(x £ 6.4)02214 (b) What is the probability that a visually impaired student gets between 6.1 and 8.33 hours of sleep? P(6.1 x

Explanation / Answer

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 ~ N(0,1)
mean ( u ) = 9.92
standard Deviation ( sd )= 1.75
a.
P(X > 6.4) = (6.4-9.92)/1.75
= -3.52/1.75 = -2.0114
= P ( Z >-2.0114) From Standard Normal Table
= 0.9779,
P(X < = 6.4) = (1 - P(X > 6.4)
= 1 - 0.9779 = 0.0221
b.
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 6.1) = (6.1-9.92)/1.75
= -3.82/1.75 = -2.1829
= P ( Z <-2.1829) From Standard Normal Table
= 0.0145
P(X < 8.33) = (8.33-9.92)/1.75
= -1.59/1.75 = -0.9086
= P ( Z <-0.9086) From Standard Normal Table
= 0.1818
P(6.1 < X < 8.33) = 0.1818-0.0145 = 0.1673
c.
P ( Z < x ) = 0.4
Value of z to the cumulative probability of 0.4 from normal table is -0.253347
P( x-u/s.d < x - 9.92/1.75 ) = 0.4
That is, ( x - 9.92/1.75 ) = -0.253347
--> x = -0.253347 * 1.75 + 9.92 = 9.476643

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

---

---

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