Question

1. If X-N (100, 42), then 68% of the data fall in what range? a. 96 - 104 b. 92 - 108 c. 88 - 104 d. 98 - 102 2. If X-N (7,02), what percent of the data fall between 7 and # – 20? a. 34% b. 47.5% C. 50% d. 95% 3. Given a normally-distributed data set whose mean is 40 and whose standard deviation is 8, what value of x would have a z-score of -1.25? a. - 10 b. 10 C. 50 d. 30

Answer 1

1. Mean = $\small \mu$ = 100

Variance =
15
= $\small 4^2$

Standard deviation= $\small \sigma$ = 4

From empirical rule we know that 68% of data lies within 1 standard deviations from the mean.

So, $\small \mu-\sigma$ = 100-4 = 96

$\small \mu+\sigma$ = 100+4 = 104

Then 68% of data fall in a) 96 - 104. (Option a)

2. The data looks like -

0.15% 2.35% 13.5% 34% 5-30 -20 -10 0.15% 34% 13.5% 2.35% *+10 +20 +30

So, we can see 34%+13.5% = 47.5% of data lies between the given interval.

Option b is correct.

3. Mean = $\small \mu$ = 40

Standard deviation= $\small \sigma$ = 8

z score = -1.25

$\small z - score=\frac{x-\mu}{\sigma}$

$\small or, \ -1.25=\frac{x-40}{8}$

$\small or, \ x=30$

Option d is correct.