Question

A frequency table was made on the ages of the sample of people using StatCrunch.

​Stat>Tables>Frequency.

Ages	0 to 20	20 to 40	40 to 60	60 to 80	80 to 100
Probability	0.295	0.523	0.157	0.024	0.001

Use the TABLE ONLY to answer the following​ questions:

What is the expected age of the sample​ taken? (Round to two decimal​ places) nothing

What is the standard deviation age of the sample​ taken? (Round to two decimal​ places) nothing

Answer 1

SOLUTION:

From given data,

A frequency table was made on the ages of the sample of people using StatCrunch.

Ages	0 to 20	20 to 40	40 to 60	60 to 80	80 to 100
Probability	0.295	0.523	0.157	0.024	0.001

Finding Mid point:

Ages	Probability P(x)	Mid point (x)
0 to 20	0.295	(0+20)/2 = 10
20 to 40	0.523	(20+40)/2 = 30
40 to 60	0.157	(40+60)/2=50
60 to 80	0.024	(60+80)/2 = 70
80 to 100	0.001	(80+100)/2 = 90

What is the expected age of the sample​ taken? (Round to two decimal​ places) nothing

The expected value = E(x) =   x * P(x)

x * P(x) = (10*0.295) + (30*0.523) + (50*0.157) + (70*0.024) + (90* 0.001)

x * P(x) =28.26

What is the standard deviation age of the sample​ taken? (Round to two decimal​ places) nothing

E(x²) =   x² * P(x) = (10²*0.295) + (30²*0.523) + (50²*0.157) + (70²*0.024) + (90²* 0.001) =1018.4

Variance = E(x²) - (E(x) )²

Variance = 1018.4 - (28.26)²

Variance = 1018.4 - 798.6276

Variance = 219.7724

The standard deviation = sqrt(Variance) = sqrt(219.7724) =14.8247 14.83