A very large gardening business grows rose bushes for sale to garden stores around the world. The most popular colors are red, pink, and white. The business decides on 50% red roses, 30% pink, and 20% white. A gardener orders 10 rose bushes selected randomly from a huge field. Her primary interest is in pink roses. A good model for the number of bushes with pink roses is given by the binomial distribution.The probability of getting at least 3 pink rose bushes is: (a) 0.5. (b) 0.617. (c) 0.348. (d) 0.259.

Complete options are;a. The approximation requires np > 10 and n(1 - p) > 10.b. The sample size here is too small to use the Normal approximation to the binomial.c. The approximation requires np > 30.d. The Normal approximation works better if the success probability p is close to p = 0.5. Answer:Option C is falseStep-by-step explanation:Looking at the options,In normal approximation to the binomial, n is the sample size,p is the given probability.q = 1 - pNow, one of the conditions for using normal approximation to the binomial is that; np and nq or n(1 - p) must be greater than 10.This means that option A is true because we require np or n(1 - p) to be greater than 10.From Central limit theorem, the sample size needs to be more than 30 for us to use normal approximation. Our sample is 10. Thus, option B is true.The approximation doesn't require np > 30. Rather it's the sample size that needs to be more than 30. Thus, option C is false.Generally, when the value of p in a binomial is close to 0.5, the normal approximations will work better than when the value of p is closer to either 0 or 1. The reason is that: for p = 0.5, the binomial distribution will be symmetrical. Thus, option D is correct.