Question

the average life span of the US population is 78 years old with a standard deviation of 4. The population is assume to be normal.

1. Find the probability that an American will live for more than 82 years.

a. .8413

b. .1587

c. .9772

d. .0228

2. Find the probability that a sample of 4 Americans will have a mean life span of more than 82

a. .8413

b. .1587

c. .9772

d. .0228

3. The approriate interpretation for the answer in the first question is:

a. The probability of an American living longer than 82 years is ....

OR

b. The probability of the mean age of 4 American is more than 82 years is ....

4. The approriate interpretation for the answer in the second question is:

a. The probability of an American living longer than 82 years is ...

OR

b. The probability of a group of 4 American will have a mean age of more than 82 years is ...

Answer 1

Solution :

Given that ,

mean = = 78

standard deviation = = 4

(1)

P(x > 82) = 1 - P(x < 82)

= 1 - P((x - ) / < (82 - 78) / 4)

= 1 - P(z < 1)

= 1 - 0.8413

= 0.1587

P(x > 82) = 0.1587

Probability = 0.1587

Option b)

2)

n = 4

= 78 and

= / n = 4 / 4 = 4 / 2 = 2

P( > 82) = 1 - P( < 82)

= 1 - P(( - ) / < (82 - 78) / 2)

= 1 - P(z < 2)

= 1 - 0.9772

= 0.0228

P( > 82) = 0.0228

Probability = 0.0228

Option d) is correct

(c)

The probability of an American living longer than 82 years is 0.1587 .

The probability of a group of 4 American will have a mean age of more than 82 years is 0.0228 .