Use an appropriate normal distribution to approximate the probability that in 1000 spins the number of times the ball lands neither on a red number nor on a black number is neither 80 or more nor less than 75.

On the roulette wheel at the Dunes Oddstacker casino, the probability of the ball landing on a red number is $\frac{6}{13}$, and the probability of the ball landing on a black number is the same.  In general, the majority of bettors will lose their bets if the ball lands neither on a red number nor on a black number.

The wheel is spun 50 times, and the ball lands on a number that is either red or black $X$ times.

Find \(P(44

In a separate experiment, the wheel is spun 1000 times and $Y$, the number of times the ball lands neither on a red number nor on a black number, is recorded.

Explain why a normal approximation would be appropriate in this case.

Due to a production error, 58% of Bobbie Sue dolls were manufactured with proportions that might be seen on a real human being.  Plastic surgeons have been buying up these so-called ‘realie’ dolls, out of a concern that if too many of them are seen by the general public then numbers of people seeking plastic surgery will decrease.

A toy shop has received an order of 100 Bobbie Sue dolls.  These may be assumed to represent a random sample.

Calculate the percentage error when an appropriate normal approximation is used to calculate probability that exactly 58 of thr 100 dolls are 'realie' dolls.