Question

1 a) Find the area of the surface obtained by rotating the circle x^2 + y^2 = 49 about the line y=7. (Keep two decimal places) (note: the answer is not 6,770.55)

b) According to the National Health Survey, the heights of adult males in the United States are
(normally distributed with mean) 73 inches, and standard deviation of 2.8 inches. What is the
probability that an adult male chosen at random is between 71 inches and 75 inches tall? (note: the answer is not 44.7)

c) The standard deviation for a random variable with probability density function f and mean μ is
defined

Find the standard deviation for an exponential density function with mean 10. (note: the answer is not 0.44)

0= [(2 – u)? f (a) der]

Answer 1

Solutions Ta Given circle x?+y= 49 Cine y = 7 ie, about x-axis Surface area is given as s=Satyds where as = + (dy je da y = Juq-xe de Tweez Vince = V1 + 2 2 2 Jug de varie S tany a Juarez e din 7 S = 147 'de = 14 JT (7+7) =141 (14) = 196 TT = 615-75216 M = 73 mean = H=73 Standard deviation - 6-9.8

a) Pl71c4c75) = P((71–73)/2.8) <(x-)/6< (75-73)/2-8) = P(-0-7142.22 0.1142) = P (220-7142) - P(22-0-7142) 70.1142 e tzte 31 de -0.74 (2.6) Visie en onze 0742 (2 .6 e 2 -0.7142 / 2) Terp (2-43 70.742 2*428)? ITT I erf 2: et! 9 *12.872) 60.7142 28 52 st S1-4.9289 +5.0 2003 = 0.18042

© The standard deviation for a random probability density function fand mean Given mean = 10. variable with is defined as f (V)-del; 20. M = 5 Oxf(x) dx = gox demax Verde i fusë tyre SEMY du)047 = -(xehte tra 3.- (hitom na te dreng-co- M4=10 f() Now, computing variance ft. | (2-w®F(1) 10 (22-24474?) +()dk

75 °*° (PA)au – su gºrf(x)dk + 1 2 1 2 Now Jº xf(x)dx = d. Jo fldx = 1 Sum of all probabilities = 1 Substituting in on = 10v2 f(1) dx=2M(m)+44 - Jouef cu seama sm xe dok je en Puple dage scou ( se * Wu) te te = Abhay + Sve "). A • E1) [w%*7*+ * (de*%)or - te U NOW Now, yoxtel) de a = Go for the age-0] +36- schienen benuta = of 1/72 Co =10. -) St Devo):10 o = 1/2 [ist devca)-10