## Related questions with answers

The frequency distribution shows the number of medical tests conducted on 30 randomly selected emergency room patients.

Number of tests performed | Number of patients |
---|---|

0 | 11 |

1 | 9 |

2 | 5 |

3 | 4 |

4 or more | 1 |

If a patient is selected at random, find these probabilities:

a. The patient had exactly 3 tests done. b. The patient had at most 2 tests done. c. The patient has 1 or 2 tests done. d. The patient had fewer than 3 tests done. e. The patient had at least 3 tests done.

Solution

VerifiedThe data given to us is for the number of items sold by a sales representative who visits customers at home.

From the data we can calculate following :

$\text{total number of home} = 8+10+3+2+1 = 24$

$\text{\textcolor{#4257b2}{\textbf{(a) }}}$ Using the formula of empirical probability, we can write the probability that exactly 1 item was sold as:

$\begin{align*} \text{P(exactly 1 item)} &= \left(\dfrac{\text{number of times she sold 1 item}}{\text{total number of homes}}\right)\\ &= \left(\dfrac{10}{24}\right)\\ \text{P(exactly 1 item)} &= \dfrac{5}{12} \end{align*}$

$\textbf{Formula for empirical probability : }$ Given a frequency distribution, the probability of an event being in a given class is :

$P(E) = \dfrac{\text{frequency for the class}}{\text{total frequencies in the distribution}} = \dfrac{f}{n}$

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