This mathematical series of puzzle caches has questions from all levels of school education, from Key Stage 1 (age 5-7) in the first few caches, all the way up to Further Maths A-Level in the last few caches. Everybody should be able to get the solutions to the first few caches, but how far through the series will you be able to get? For a full description of the series, please see the first cache “1+1=1”. If you can’t solve a particular set of questions, try asking somebody of the appropriate age, or your friendly neighbourhood Maths teacher!
Please note that many of the caches are hidden near busy roads, so please take care when finding them, especially if you have children with you. It is worth noting that there is parking possible within a few hundred metres of all caches and a quick look on a satellite view map should show suitable places.
This cache contains questions from the A-Level Further Maths course, from the Statistics modules.
1. The continuous random variable has the cumulative distribution function defined by these three parts: F(y)=0 for y<0, F(y)=(1/4)(y^3-4Y^2+ky) for 0<=y<=2, F(y)=1 for y>2. P(y>1)=0.2A. Find A.
2. A politician, Mr Muggle, claims that 45% of people would vote for him in an election. N people are selected at random for an opinion poll, and none of them said that the would vote for him. Using a 1% level of significance, B=the smallest value of N for which the null hypothesis, p=0.45, will be rejected in favour of the alternate hypothesis, p<0.45.
3. A gps manufacturer finds that the life expectancy of its units has a standard deviation of 5000 hours of use. On a random sample of 100 worn out units, it finds that the total hours of use for all units is 1740000 hours. If the 95% confidence interval for the mean lifetime of a unit is written as [p,q], C=(q-p)/140.
4. At an event cache, the male cachers have heights which follow a normal distribution with mean 177cm and a standard deviation of 5. The female cachers heights also follow a normal distribution, but with a mean of 163cm and a standard deviation of 4. A male and a female cacher are chosen at random. When written to 2 decimal places, the probability that the male cacher is taller than the female cacher is 0.9D. Find D.
5. The width of 35mm film canisters is found to be normally distributed with mean Wmm and a standard deviation of 0.5mm. The probability that a randomly selected canister is within 0.6mm of W is 0.E698. Find E.
The cache can be found at N50 45.PQR E0 12.STU where P=A+1, Q=B-E, R=C-D, S=C-A, T=C-B, U=E+2
You can check your answers for this puzzle on GeoChecker.com.