<p>Each month the amount of electricity, $X$ measured in kilowatt-hours (kWh), used by a household in a particular city may be assumed to follow a normal distribution with mean $950$ and standard deviation $\sigma $ . The charge for electricity used per month is fixed at $\$0.22$ per kWh.</p>
<ol class="i-list"><li><div class="list-item-paragraph">Given that $65\%$ of the households uses less than $960$ kWh of electricity in a month, find the value of $\sigma $, correct to $1$ decimal place.</div><p style="text-align: right;">[2]</p></li></ol>
<p>For the rest of the question, $\sigma $ is the value found in part <strong>(i)</strong>.</p>
<ol class="i-list" start="2"><li><div class="list-item-paragraph">Find the probability that the difference in the amount of electricity used among $2$ randomly chosen households in a particular month is not more than $30$ kWh.</div><p style="text-align: right;">[3]</p></li><li><div class="list-item-paragraph">In the month of August, the mayor of the city decides to provide $50\%$ and $30\%$ subsidies for the electricity bills of households in the North and South districts of the city respectively. Find the probability that the total electricity bill of $2$ randomly chosen North district households and $1$ South district household is less than $\$360$.</div><p style="text-align: right;">[4]</p></li><li><div class="list-item-paragraph">In December, a random sample of n households is chosen to study the mean monthly electricity usage per household in the city. Find the least value of n if the probability of the sample mean being less than $955$ kWh is at least $0.9$.</div><p style="text-align: right;">[3]</p></li></ol>

Each month the amount of electricity, $X$ measured in kilowatt-hours (kWh), used by a household in a particular city may be assumed to follow a normal distribution with mean $950$ and standard deviation $\sigma $ . The charge for electricity used per month is fixed at $\$0.22$ per kWh.

Given that $65\%$ of the households uses less than $960$ kWh of electricity in a month, find the value of $\sigma $, correct to $1$ decimal place.

For the rest of the question, $\sigma $ is the value found in part **(i)**.

Find the probability that the difference in the amount of electricity used among $2$ randomly chosen households in a particular month is not more than $30$ kWh.

In the month of August, the mayor of the city decides to provide $50\%$ and $30\%$ subsidies for the electricity bills of households in the North and South districts of the city respectively. Find the probability that the total electricity bill of $2$ randomly chosen North district households and $1$ South district household is less than $\$360$.

In December, a random sample of n households is chosen to study the mean monthly electricity usage per household in the city. Find the least value of n if the probability of the sample mean being less than $955$ kWh is at least $0.9$.

2017 RVHS P2 Q10

2017 RVHS P2 Q10

Video Solution: