In a survey it is found that barn owls occur randomly at a rate of 9 per \(1000 \mathrm {~km} ^ { 2 }\).
Find the probability that in a randomly selected area of \(1000 \mathrm {~km} ^ { 2 }\) there are at least 10 barn owls.
Find the probability that in a randomly selected area of \(200 \mathrm {~km} ^ { 2 }\) there are exactly 2 barn owls.
Using a suitable approximation, find the probability that in a randomly selected area of \(50000 \mathrm {~km} ^ { 2 }\) there are at least 470 barn owls.
The proportion of houses in Radville which are unable to receive digital radio is \(25 \%\). In a survey of a random sample of 30 houses taken from Radville, the number, \(X\), of houses which are unable to receive digital radio is recorded.
Find \(\mathrm { P } ( 5 \leqslant X < 11 )\)
A radio company claims that a new transmitter set up in Radville will reduce the proportion of houses which are unable to receive digital radio. After the new transmitter has been set up, a random sample of 15 houses is taken, of which 1 house is unable to receive digital radio.
Test, at the \(10 \%\) level of significance, the radio company's claim. State your hypotheses clearly.