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Question

1) In a study of 420,095 cell phone users in Denmark, it was found that 135 developed cancer of the brain or nervous system. If we assume that the use of cell phone has no effect on developing such cancer, then the probabilty of a person having such a cancer is 0.000340.

Assuming that cell phone have no effect on developing cancer, find the mean and standard deviation for the numbers of people in groups of 420,095 that can be expected to have cancer of the brain or nervous system.

2) The CIA has specialists who analyze the frequenencies of letters of the alaphabet in an attempt to decipher intercepted message that are sent as ciphered text. In standard English text, the letter r is used at rate of 6%

Find the mean and standard deviation for the number of times the letter r will be found on a typical page of 2600 characters.

3)Based on a Harris poll of 370 adults who regret getting tattoos, 20% say that they were too young when they got their tattoos.

For randomly selected group of 370 adults who regreet getting tattoos, find the mean and standard deviation for the number who say that they were too young when they got their tattoos.

For the following question, ignore leap year

4) For classes of 30 students, find the mean and standard deviation for the number born on the 4th of July. Express results using seven decimal places.

Answer 1

(1)

Step 1:

A survey had conducted with 420,095 cell phone users.

it was found that 135 developed cancer of the brain or nervous system.

Survey says that probability of a person having cancer is 0.000340.

Find the mean.

Here number of samples n = 420095.

Probability of a person having cancer is p = 0.000340.

Since it follows binomial distribution,

Mean .

Where n is number of samples,

             p is probability of success.

Step 2:

Find the standard deviation.

Standard deviation .

Where n is number of samples,

             p is probability of success,

             q is probability of failure.

Probability of failure q = 1 - p.

q = 1 - 0.000340

q = 0.99966.

Solution:

Mean is 142.8323 .

Standard deviation is 11.949.

 

 

 

 

 

 

Answer 2

(2)

Step 1:

CIA had analyze the frequencies of letters of the alphabet.

They had examine the 2600 characters on o page.

They found that the letter r is used at rate 6% .

Find the mean.

Here number of samples n = 2600.

Probability of letter r  is  .

Since it follows binomial distribution,

Mean .

Where n is number of samples,

             p is probability of success.

Step 2:

Find the standard deviation.

Standard deviation .

Where n is number of samples,

             p is probability of success,

             q is probability of failure.

Probability of failure q = 1 - p.

q = 1 - 0.06

q = 0.94.

Solution:

Mean is 156 .

Standard deviation is 12.11.

 

 

 

 

 

 

Answer 3

(3)

Step 1:

In Harris poll  370 adults are regret getting tattoos.

Based on this poll 20%  say that they were too young to get tattoos.

Find the mean.

Here number of samples n = 370.

Probability of adults who regret tattoos  is  .

Since it follows binomial distribution,

Mean .

Where n is number of samples,

             p is probability of success.

Step 2:

Find the standard deviation.

Standard deviation .

Where n is number of samples,

             p is probability of success,

             q is probability of failure.

Probability of failure q = 1 - p.

q = 1 - 0.2

q = 0.8.

Solution:

Mean is 74 .

Standard deviation is 7.69.

 

 

 

 

 

 

 

 

 

Answer 4

(4)

Step 1:

The total number of students in a class is 30.

The number of days in a general year is 365 days.

The probability of the student born on the 4th July is  .

Find the mean.

Here number of samples .

Probability of the student born on the 4th July is .

Since it follows the binomial distribution,

Mean .

Where n is number of samples.

          p is probability of success.

Step 2:

Find the standard deviation.

Standard deviation .

Where n is number of samples.

         p is probability of success.

         q is probability of failure.

Probability of failure is

Solution :

Mean is .

Standard deviation is .