Question

Given a mean of 43.8 and a standard deviation of 8.7, within how many standard deviations of the mean do the values 60, 40, 35, 45, and 39 fall?

Answer 1

I think the answer is 0.

Answer 2

Answer with explanation:

Mean ($\mu$) = 43.8

Standard Deviation ($\sigma$) = 8.7

We can draw the normal curve and then show where these values lie.

Or we can use the equation, $43.8 \pm 8.7 \times k = \text{Value}$, use positive sign when ,number is greater than mean, and negative sign when number is smaller than mean, to find that , how many standard deviations of the mean do the values 60, 40, 35, 45, and 39 fall.

1.→ 43.8 +8.7 k= 60

8.7 k= 60 - 43.8

8.7 k= 16.2

$k=\frac{16.2}{8.7}\\\\k=1.8620\\\\k=1.86$

2.→ 43.8 - 8.7 k=40

43.8-40 = 8.7 k

8.7 k= 3.8

$k=\frac{3.8}{8.7}\\\\k=0.4367\\\\k=0.44$

3.→43.8 - 8.7 k=35

43.8-35 = 8.7 k

8.7 k= 8.8

$k=\frac{8.8}{8.7}\\\\k=1.011\\\\k=1.01$

4.→43.8 + 8.7 k=45

43.8-45 = -8.7 k

-8.7 k= -1.2

8.7 k= 1.2

$k=\frac{1.2}{8.7}\\\\k=0.1379\\\\k=0.14$

5.→43.8 -8.7 k=39

43.8-39 = 8.7 k

8.7 k= 4.8

$k=\frac{4.8}{8.7}\\\\k=0.5517\\\\k=0.55$