Question

12. Using a normal distribution and z score formula answer the following questions: a. Find the Z-score that cuts off the top 35% of the nornval curve b. Find the data value to the nearest whole number that cuts off the bottom 20% of the curve given that the mean is 75 and sample standard deviation is 5. c. Find the z scores that cut off the middle 50% of the normal curve.

Answer 1

12) a) Let Z (ره) یہ have to that the z Score find off top 357. Normal wts of the orve. let the point be So, P(Z <x) = -0.35= 0.65 =) P(Z <x) = 0.65 :-) 0 (~) = (0.38531) x = 0.38531. z score That 357. The top So, the of the cuts is Normal curve 0.38531 b) are given which follows with random variable à Normal distribution and standard deviation mean 75 X be random variable. Let X~ N(75, (52) to have to find the nearest whole which cots the number 207, we bottom corve. of the Let (he be y 0.26 0.20 point P(x = y) => PC x-75 L 4-75) $(4-1)-7--048) X - 75 5 ... X~ N(75, (53²) Ern(0,1)] Po is CBF of N(o,) 5

=) Y-75 = -0.84 16 3 5 => y = 75+ (5 -0,84163) - 70.79185. so, the point is 70.79185 The nearest whole number closest to the point is 71 N on Z ~ N(0,1) have to find the z cots the middle 5.0 % scores which of the corve. Normal 50% + -2 corve here is NOW Normal about symmetric then the let the upper point be x² lower point is p(-x2 <Z2x) = 0.50 3) (x) - (-x) = 0.50 [ $(2) + § (7) > P(x) - (1 - $(x)) = 0.50 2 § (x) - 1 = 0.50 ']

20 () - 1.50 ©(x) = 0.75 = (0.6745) > =) x = 0.6745. So the Z scores That wt off the middle are The curie 50% of the - 0.6745 and 0.6745