Continuous probability

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