Question

3) Statement 3: a) What is the numerical value for the lower bound (LB) of the interval? b) What is the numerical value for the upper bound (UB) of the interval? c) We are interested in P(LB<Z <UB). Complete the sketch for this probability. ~99.7% of the observations will lie within 3ơ 0 d) Find P(LB<Z<UB). Be sure to write the probability in terms of cumulative probabilities.

Answer 1

It is given that 99.7% of the observations will lie within $\mu \pm 3 \sigma$ .

a.

The numerical value for the lower bound (LB) of the interval is $\mu - 3 \sigma$.

b.

The numerical value for the upper bound (UB) of the interval is $\mu &plus; 3 \sigma$ .

c.

We have to find P(LB < Z < UB). The normal curve for it is as follows:

d.

To find P(LB < Z < UB) = P(Z < UB) - P(Z < LB)

= P(Z < $\mu &plus;3 \sigma$ ) - P (Z < $\mu - 3 \sigma$)

= 0.997

= 99.7%