Question

The mean of a normal probability distribution is 320; the standard deviation is 18.

a)About 68% of the observations lie between what two values? Value #1_____. Value #2______.

b)About 95% of the observations lie between what two values? Value#1_____. Value#2_____.

c)Practically all of the observations lie between what two values? Value#1______. Value#2______.

Answer #1

**Answer:**

Given,

mean = 320 &

Standard deviation( sd) =16

a)

Since from the standard definition,

we know that the about 68% of the values fall between 1 SD of the mean

so interval is 320 16

= (320 - 16, 320+16)

= (304,336)

**so they fall between 304 and 336**

b)

68% of the values fall between 2 SD of the mean

= 320 16*2

= (320 32)

= (320-32, 320+32)

= **(288 ,352)**

c)

practically all the values fall within 3 Standard deviation of mean

320 16*3

= 320 48

= (320 - 48, 320+48)

**= (272 , 368)**

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