Question

A sample of size 29 will be drawn from a population with mean 108 and standard deviation 32.

(a) Is it appropriate to use the normal distribution to find probabilities for x?

(b) If appropriate find the probability that x will be less than 88.

(c) If appropriate find the 80th percentile of x.

.

Answer 1

a)

yes, it is appropriate because n = 29 , mea = 108 , s = 32 is given

b)

Here, μ = 108, σ = 5.9423 and x = 88. We need to compute P(X >= 88). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (88 - 108)/5.9423 = -3.37

Therefore,
P(X <= 88) = P(z <= (88 - 108)/5.9423)
= P(z <= -3.37)
= 0.0004

c)

z value at 80% = 0.84

z =(x - mean)/s

0.84 = (x - 108)/5.9423

x = 5.9423 * 0.84+ 108

x = 112.99