Question

6. Find the median for the standard normal distribution. (Keep 2 decimals)

7. Find IQR for the standard normal distribution. (Keep 2 decimals)

8. P(|Z|> 1.15)

9. Let X ~ N(216; 24). Find:

(a) P(X <= 241)

(b) P(175 < X < 226)

(c) The first quartile for X

(d) The third quartile for X

(e) the IQR for X

(f) P(|X-216|> 39)

Answer 1

(6)

Median for the standard normal distribution is 0.00 because in the case of the standard normal distribution, the mid value divides the distribution into 2 equal halves and thus mean, median and mode coincide.

Thus,

Answer is:

0.00

(7)

Q1 = First Quartile is value of Z for which area from mid value of Z on LHS = 0.025.

Table of Area Under Standard Normal Curve gives Z = - 0.675

Q3 = Third Quartile is value of Z for which area from mid value of Z on RHS = 0.025.

Table of Area Under Standard Normal Curve gives Z = 0.675

So,

IQR = Q3 - Q1 = 0.675 + 0.675 = 1.35

So,

Answer is:

1.35

(8)

For Z = 1.15, Table of Area Under Standard Normal Curve gives area = 0.3749

So,

P(|Z|> 1.15) = (0.5 - 0.3749) X 2 = 0.2502

So,

Answer is:

0.2502

(9)

= 216

= 24

To find P(X241):
Z = (241 - 216)/24

= 1.0417

By Technology, Cumulative Area Under Standard Normal Curve = 0.8512

So,

P(X241):= 0.8512

So,

Answer is:

0.8512

(b)

To find P(175 < X < 226):
For X = 175:

Z = (175 - 216)/24

= - 1.7083

By Technology, Cumulative Area Under Standard Normal Curve = 0.0438

For X = 226:

Z = (226 - 216)/24

= 0.4167

By Technology, Cumulative Area Under Standard Normal Curve = 0.6616

So,

P(175 < X < 226):= 0.6616 - 0.0438 = 0.6178

So,

Answer is:

0.6178

(c)

Q1 = First Quartile is value of Z for which area from mid value of Z on LHS = 0.025.

Table of Area Under Standard Normal Curve gives Z = - 0.675

So,

Z = - 0.675 = (X - 216)/24

So,

X = 216 - (0.675 X 24)

= 216 - 16.2

=199.80

So,

Answer is:

199.80

(d)

Q3 = Third Quartile is value of Z for which area from mid value of Z on RHS = 0.025.

Table of Area Under Standard Normal Curve gives Z = 0.675

So,

Z = 0.675 = (X - 216)/24

So,

X = 216 + (0.675 X 24)

= 216 + 16.2

=232.20

So,

Answer is:

232.20

(e)

IQR = Q3 - Q1 = 232.20 - 199.80 = 32.40

So,

Answer is:

32.40

(f)

Z = 39/24= 1.625. Table gives area = 0.4484. So, required probability = (0.5 - 0.4484) X 2 = 0.1032. So,Answer is: 0.1032