7. A company makes cricket balls and tennis balls.
The weights of cricket balls, \(C\) grams, follow a normal distribution
$$C \sim \mathrm {~N} \left( 160,1.25 ^ { 2 } \right)$$
Three cricket balls are selected at random.
- Find the probability that their total weight is more than 475.8 grams.
The weights of tennis balls, \(T\) grams, follow a normal distribution
$$T \sim \mathrm {~N} \left( 60,2 ^ { 2 } \right)$$
Five tennis balls and two cricket balls are selected at random.
- Find the probability that the total weight of the five tennis balls and the two cricket balls is more than 625 grams.
A random sample of \(n\) tennis balls \(T _ { 1 } , T _ { 2 } , \ldots , T _ { n }\) is taken.
The random variable \(Y = ( n - 1 ) T _ { 1 } - \sum _ { r = 2 } ^ { n } T _ { r }\)
Given that \(\mathrm { P } ( Y > 40 ) = 0.0838\) correct to 4 decimal places, - find \(n\).
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