The mean incubation time for a type of fertilized egg kept at a certain temperature is 21 days. Suppose that the incubation times are approximately normally distributed with a standard deviation of 1 day. Complete parts (a) through (e) below. Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). (a) Draw a normal model that describes egg incubation times of these fertilized eggs. Choose the correct graph below. Click here to view graph a O Click here to view graphd. O Click here to view graph c. O Click here to view graphb. (b) Find and interpret the probability that a randomly selected fertilized egg hatches less than 19 days. The probability that a randomly selected fertilized egg hatches in less than 19 days isN. (Round to four decimal places as needed.) Interpret this probability. Select the correct choice below and fill in the answer box to complete your choice. O A. In every group of 100 fertilized eggs. eggs will hatch in less than 19 days. (Round to the nearest integer as needed.) O B. The average proportion of the way to hatching of all eggs fertilized in the past 19 days is (Round to two decimal places as needed.) OC. If 100 fertilized eggs were randomly selected, of them would be expected to hatch in less than 19 days. (Round to the nearest integer as needed.) (c) Find and interpret the probability that a randomly selected fertilized egg takes over 23 days to hatch. The probability that a randomly selected fertilized egg takes over 23 days to hatch is (Round to four decimal places as needed.) Interpret this probability. Select the correct choice below and fill in the answer box to complete your choice. O A. In every group of 100 fertilized eggs. eggs will hatch (Round to the nearest integer as needed.) more than 23 days. O B. The average proportion of the way to hatching of all eggs fertilized more than 23 days ago is (Round to two decimal places as needed.)
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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