Answer:
[tex]\begin{array}{ccc}{Class} & {Frequency} & {Relative\ Frequency} &{30-39} & {1} & {0.025} & {40-49} & {1} & {0.025} & {50 - 59} & {2} & {0.050} & {60 - 69} & {5} & {0.125} & {70 - 79} & {13} & {0.325} & {80 - 89} & {10} & {0.250} & {90 - 99} & {8} & {0.200} &{Total} & {40} & {1}\ \end{array}[/tex]
[tex]P(x < 70) = 0.225[/tex]
Step-by-step explanation:
Given
[tex]Lower = 30[/tex]
[tex]Width = 10[/tex]
Solving (a): The relative frequency table
First, we construct the frequency table using the given parameters.
[tex]\begin{array}{cc}{Class} & {Frequency} &{30-39} & {1} & {40-49} & {1} & {50 - 59} & {2} & {60 - 69} & {5} & {70 - 79} & {13} & {80 - 89} & {10} & {90 - 99} & {8} & {Total} & {40}\ \end{array}[/tex]
The relative frequency (RF) is calculated as:
[tex]RF = \frac{Frequency}{Total}[/tex]
Using the above formula to calculate the relative frequency, the relative frequency table is:
[tex]\begin{array}{ccc}{Class} & {Frequency} & {Relative\ Frequency} &{30-39} & {1} & {0.025} & {40-49} & {1} & {0.025} & {50 - 59} & {2} & {0.050} & {60 - 69} & {5} & {0.125} & {70 - 79} & {13} & {0.325} & {80 - 89} & {10} & {0.250} & {90 - 99} & {8} & {0.200} &{Total} & {40} & {1}\ \end{array}[/tex]
Solving (b): [tex]P(x < 70)[/tex]
To do this, we add up the relative frequencies of classes less than 70.
i.e.
[tex]P(x < 70) = [30 - 39] + [40 - 49] + [50 - 59] + [60 - 69][/tex]
So, we have:
[tex]P(x < 70) = 0.025 + 0.025 + 0.050 + 0.125[/tex]
[tex]P(x < 70) = 0.225[/tex]
