can you please help me solve this

Question

If a seed is planted, it has a 46% chance of growing into a healthy plant. Let X be the number of seeds grow into healthy plants when 62 seeds are planted.

1. What is the distribution of X? X ~ ? B U N  (,) 
2. Please show the following answers to 4 decimal places.
3. What is the probability that exactly 32 seeds grow into healthy plants? 
4. What is the probability that less than 32 seeds grow into healthy plants? 
5. What is the probability that more than 32 seeds grow into healthy plants? 
6. What is the probability that between 17 and 37 (including 17 and 37) seeds grow into healthy plants? 

Answer 1

You know that this is a binomial distribution with a size of 62, and a success probability of 0.46.

1. What is the probability that exactly 32 seeds grow into healthy plants?  0.06825

For part 4 to part 6, either you have to calculate directly, or you can use a normal approximation. To claim that this binomial can be approximated by a normal distribution with a mean 0.46*62 = 28.52 and variance 0.46*62*0.54 = 15.4008.