Problem 6RE

In Exercises , refer to the table in the margin. The random variable x is the number of males with tinnitus (ringing ears) among four randomly selected males (based on data from “Prevalence and Characteristics of Tinnitus among US Adults” by Shargorodsky et al,American Journal of Medicine, Vol. 123, No. 8).

Tinnitus Find the mean and standard deviation for the random variable x. Use the range rule of thumb to identify the range of usual values for the number of males with tinnitus among four randomly selected males. Is it unusual to get three males with tinnitus among four randomly selected males?

Problem 6RE

Answer:

Step1 of 1:

We have n = 4

S = {male, female}

Probability of getting male P(male) = = = 0.5

Similarly, Probability of getting female P(female) = = = 0.5

Hence, p = 0.5.

Consider a random variable “x” follows binomial distribution with sample size “n” and proportion “p”.

i,e.X B(n, p)

Where,

n = 16 and p = 0.10.

q = 1 - p

= 1 - 0.10

= 0.90.

Probability mass function of binomial distribution is given by

P(x) = , x = 0,1,2,...,n.

x |
P(x) |
xP(x) |
P(x) |

0 |
0.645 |
0 |
0.091673 |

1 |
0.280 |
0.28 |
0.108676 |

2 |
0.044 |
0.088 |
0.115902 |

3 |
0.003 |
0.009 |
0.02064 |

4 |
0.000 |
0 |
0 |

= 0.377 |
= 0.336891 |

Therefore, mean of the binomial distribution is given by

= 0.377.

Standard deviation of the binomial distribution is given by

= 0.337.