The Alioto Fish Market on the San Francisco Pier wants to determine the probability that a randomly selected blue crab has a weight greater than 1 kg. Assume that the distribution of weights (kg) of adult blue crabs is normally distributed with a population mean (μ) of 0.8 kg and a standard deviation (σ) of 0.3 kg. What is the probability that a randomly selected adult blue crab will weigh more than one kilogram?
Mean Weight = 0.8 kg
Standard Deviation =0.3
Weight target = 1 kg
Step one requires you to find the z score for this problem using the z score formula:
1.0 minus 0.8 divided by the standard deviation (0.3) yields a z-score of 0.67
Now, look up the numbers 0.67 + and minus which yields scores of .7486 (upper) and .2514 (lower)
Since we are looking trying to find the probability of a randomly selected blue crab weighing more than 1 kg, the answer is as follows:
.7486 .2514
_-3___-2___-1____0_______1_____2_____3___
0.67
Therefore, the probability of finding a randomly selected blue crab weighing more than 1 kg is .2514. Not very high.
The following questions and exercises are directly related to the achievement of the objectives stated for Weeks 2 and 3. Please answer the items below and submit them as part of your Week 3 Individual assignment:
1. Southwest Airlines wanted to improve its on-time arrival in the month of July. Its average time for June was 10.45 minutes per flight with a standard deviation of 1.87 minutes. What is the probability that their on-time arrivals will be less than nine minutes in July?
______________
2. McBurgers Restaurant claimed that they could provide anything on the menu in three minutes. A survey of 1000 customers yielded the following data. Mean 5.71 minutes with a standard deviation of 1.02 minutes.
______________ What is the probability that McBurgers could provide a meal in less than 4 minutes?
______________ What is the probability that McBurgers could provide a meal in more than 5 minutes?
3. Which statement is not true about a binomial distribution:
A. _____ Each trial can result in just two possible outcomes.
B. _____ the number of times an event occurs in an interval
C. ______ n represents repeated trials
D. ______ The probability of success, denoted by P, is the same on every trial.
4. The revenues for one week at the Bon Appetite Café are as follows:
Monday 10,345
Tuesday 11,212
Wednesday 9, 763
Thursday 10,554
Friday 9,899
Saturday 11,239
Sunday 8,732
Calculate a confidence interval at the 99% level and explain what it might represent to the owners