Question

In: Statistics and Probability

The Weights of 100 remote control cars at a competition are approximately normally distributed. The average...

The Weights of 100 remote control cars at a competition are approximately normally distributed. The average weight is 3.2 kg, with a standard deviation of 0.4 kg. a.) How many remote control cars would be disqualified if it were against the rules to have a car with a weight of more than 4 kg or less than 2.4 kg? b.) A car is said to be in the 90^th percentile. How much does it weigh?

Expert Solution

A) P(X > 4) + P(X < 2.4)

= P((X - )/ > (4 - )/) + P((X - )/ < (2.4 - )/)

= P(Z > (4 - 3.2)/0.4) + P(Z < (2.4 - 3.2)/0.4)

= P(Z > 2) + P(Z < -2)

= (1 - P(Z < 2)) + P(Z < -2)

= (1 - 0.9772) + 0.0228

= 0.0456

Number of remote control cars would be disqualified = 100 * 0.0456 = 4.56 = 5

B) P(X < x) = 0.9

Or, P((X - )/ < (x - )/) = 0.9

Or, P(Z < (x - 3.2)/0.4) = 0.9

Or, (x - 3.2)/0.4 = 1.28

Or, x = 1.28 * 0.4 + 3.2

Or, x = 3.712

orchestra answered 2 years ago

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