Question

a). How can I Construct a tally table to represent the data ? b).How can I calculate the probability that if a student is chosen at random that he/she is i). not more than 153cm in height ii)greater than 153cm in height.

Answer 1

Write out the data given

To construct a frequency table, we write out the data and obtain thier frquency.

The data ranges from 150 to 156, we write 150 to 156 vertically,

The probability of an event is given by the required outcome of the total outcome,

`\begin{gathered} \text{ Where total outcome =150} \\ \text{required outcome = frequency of the data required } \end{gathered}`

Hence, the probabilty that the height of the student is not more that 153 will be

`Pr(x\le153)=Pr(x=150)+Pr(x=151)+Pr(x=152)+Pr(x=153)`

Where

`\begin{gathered} Pr(150)=(1)/(50),Pr(151)=(5)/(50) \\ \\ Pr(152)=(10)/(50),Pr(153)=(16)/(50) \end{gathered}`

Then, take the sum of the probability, we have

`Pr(x\le153)=(1)/(50)+(5)/(50)+(10)/(50)+(16)/(50)=(1+5+10+16)/(50)=(32)/(50)=0.64`

hence

The probability that if a student is chosen at random that he/she is not more than 153cm in height is 32/50 or 0.64

Similartly, The probability that the height is greater than 153 will be

`\begin{gathered} 1-\text{Probability is not more that 153} \\ 1-Pr(x\le153) \\ 1-(32)/(50)=(50)/(50)-(32)/(50)=(18)/(50) \\ \text{then} \\ Pr(x>153)=(18)/(50)=0.36 \end{gathered}`

Hence

The probability that the height is greater than 153 in height is 18/50 or 0.36