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. Probability calculations are quicker when using the Normal approximation to the binomial distribution. Which of the following is false a. The approximation requires np 10 and n(1 â 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.

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.

Option C is false

Step-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 - p

Now, 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.

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.