The weights of pineapples grown are approximately normally distributed with a standard deviation of 2.5 and mean of 31 ounces. Suppose a single pineapple is selected at random.
a. If a single pineapple is selected at random, what is the approximate probability that it weighs more than 35 ounces?
b. Suppose 2 pineapples are randomly and independently selected. Find the probability that exactly 1 of the 2 pineapples weighs more than 35 ounces.
c. If you select pineapples at random from the crop, how many pineapples might you have to inspect before you find one that weighs more than 35 ounces?
1. Design a simulation using a random digits table to mimic the search for a suitable pineapple.
2. Perform the simulation twice, clearly illustrating the procedure and the results. Begin on line 127 of Table B.
d. Find the probability that your 1st suitable pineapple (weighing 35 or more ounces) is one of the first 2 pineapples you inspect.
Managers were eager to test a new irrigation system and did so during this year’s production cycle.
e. How large a sample would you need to take to estimate the mean weight of the pineapples produced to within 1 ounce at a 95% confidence level?
f. Use a 95% confidence interval to determine whether this sample provides evidence of a change in the mean weight of pineapples produced. Explain.
g. Did the new irrigation system cause an increase in the mean weights of pineapples produced? Explain.
We do not do your homework for you. However, I will start you out.
a. Z = (x - mean)/standard deviation
Once you find the Z score, look it up in a table in the back of your stats text. The smaller portion column will give you the desired proportion.
I hope this helps.