Question

Buoyancy aids in watersports are tested by adding increasing weights until they sink. A

club has two sets of buoyancy aids. One set is two years old, and should support weights

according to 𝑁(6.0,0.64)kg, the other set is five years old and should support weights of

𝑁(4.5, 1.0) kg. all the aids are tested and any which are unable to spport at least 5kg are

thrown out.

a. If there are 24 two-year aids, how many are still usable?

b. If there are 32 five-year old aids how many are still usable?

Answer 1

a.

$$P(X>5)=1-P(Z\le\dfrac{5-6}{\sqrt{0.64}})$$

$$=1-P(Z\le-1.25)=0.89435$$

$$0.89435(24)=21$$

21 buoyancy aids.

b.

$$P(X>5)=1-P(Z\le\dfrac{5-4.5}{\sqrt{1.0}})$$

$$=1-P(Z\le0.5)=0.30854$$

$$0.30854(32)=10$$

10 buoyancy aids.