| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Bivariate data |
| Type | Interpret correlation coefficient value |
| Difficulty | Moderate -0.8 This is a straightforward application of normal distribution with standard procedures: finding probabilities using z-scores, calculating expected values, and working backwards from a probability to find standard deviation. All parts use routine techniques covered early in S1 with no novel problem-solving required. The question is slightly easier than average due to its step-by-step structure and reliance on direct formula application. |
| Spec | 2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation |
8. The lifetimes of bulbs used in a lamp are normally distributed.
A company $X$ sells bulbs with a mean lifetime of 850 hours and a standard deviation of 50 hours.
\begin{enumerate}[label=(\alph*)]
\item Find the probability of a bulb, from company $X$, having a lifetime of less than 830 hours.
\item In a box of 500 bulbs, from company $X$, find the expected number having a lifetime of less than 830 hours.
A rival company $Y$ sells bulbs with a mean lifetime of 860 hours and $20 \%$ of these bulbs have a lifetime of less than 818 hours.
\item Find the standard deviation of the lifetimes of bulbs from company $Y$.
Both companies sell the bulbs for the same price.
\item State which company you would recommend. Give reasons for your answer.\\
\begin{table}[h]
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\caption{}
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\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q8}}