Question

1. A new breed of avocados has weights that are normally distributed with mean of µ = 110 grams and population standard deviation σ = 16 grams.

(a) What is the probability that any one randomly chosen avocado would have a weight of 120 grams or above? Shade the appropriate region in the normal distribution plot. Be sure to plot and label the observed weight on the horizontal axis. Also label the center of the distribution with the appropriate value.

(b) The heaviest 15% of avocados are sold at a higher price, as jumbo avocados. What is the weight cut-off for jumbo avocados?

(c) What is the probability that a randomly selected avocado has a weight between 90 grams and 115 grams?

(d) A local market sells avocados in bags of 10. Avocados are randomly assigned to bags. What is the probability that a randomly selected bag of 10 avocados will have an average weight above 120 grams?

Answer 1

1. Here it is given that distribution is normal with mean=110 and standard deviation=16

a. We need to find

As distribution is normal we can convert x to z

b. Here we need to find x such that

Using z table we get

So

So

c. Here we need to find

d. Here population is normal so as per central limit theorem distribution of sample mean is also normal

We need to find

As sample mean is normal we can convert sample mean to z