A-LevelMathematicsProbability and statistics9709/62 · Feb/Mar 2022 · Q35 Marks
A random sample of 500 households in a certain town was chosen. Using this sample, a confidence interval for the proportion, p, of all households in that town that owned two or more cars was found to be 0.355 < p < 0.445. Find the confidence level of this confidence interval. Give your answer correct to the nearest integer.
- Find the confidence level of this confidence interval. Give your answer correct to the nearest integer.[5]
Mark scheme
Marking points from the official mark scheme (Feb/Mar 2022). The mark or mark type is shown in brackets.
- [B1] est(p) = 0.4
- [M1] OE. Use of their 0.4 in a correct expression
- [A1] z = 0.045÷√('0.4'×(1-'0.4')/500) = 2.054 Condone 2.053 and 2.05
- [M1] 0.98 - (1-0.98)
- [A1] 96% confidence CWO, must be integer
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