i need help with this please

Question

Suppose that the weight of seedless watermelons is normally distributed with mean 6 kg. and standard deviation 1 kg. Let X be the weight of a randomly selected seedless watermelon. Round all answers to 4 decimal places where possible.

a. What is the distribution of X? X ~ N(,)

b. What is the median seedless watermelon weight?  kg.

 

c. What is the Z-score for a seedless watermelon weighing 6.6 kg? 

d. What is the probability that a randomly selected watermelon will weigh more than 6.1 kg? 

e. What is the probability that a randomly selected seedless watermelon will weigh between 5.3 and 6.1 kg? 

f. The 85th percentile for the weight of seedless watermelons is  kg.

Answer 1

a) distribution is N(6,1)

b) for normal distribution median = mean

c) if x = a seedless watermelon weight, z score = (x - mean)/standard deviation

d) Compute z-score for x = 6.1 then find P(z > z-score)

e) Compute z-score#1 for x = 6.1 and z-score #2 for x = 5.3 then find P(z < z-score # 1) - P(z < z-score # 2).

f) Determine z-score associated with 85% percentile. Solve for x: z-score 85th percentile = (x - mean)/standard deviation.