Moderate -0.5 This is a straightforward inverse normal distribution problem requiring students to use standard normal tables to find the z-score corresponding to 1% (z ≈ -2.326), then solve 250 = 260 + (-2.326)σ for σ. It's slightly easier than average because it's a direct application of a standard technique with no conceptual complications, though it does require correct use of tables and algebraic manipulation.
1 Packets of tea are labelled as containing 250 g . The actual weight of tea in a packet has a normal distribution with mean 260 g and standard deviation \(\sigma \mathrm { g }\). Any packet with a weight less than 250 g is classed as 'underweight'. Given that \(1 \%\) of packets of tea are underweight, find the value of \(\sigma\). [3]
1 Packets of tea are labelled as containing 250 g . The actual weight of tea in a packet has a normal distribution with mean 260 g and standard deviation $\sigma \mathrm { g }$. Any packet with a weight less than 250 g is classed as 'underweight'. Given that $1 \%$ of packets of tea are underweight, find the value of $\sigma$. [3]
\hfill \mbox{\textit{CAIE S1 2014 Q1 [3]}}