The size of fish is very important to commercial fishing. A study conducted in 2012 found the length of Atlantic cod caught in nets in Karlskrona to have a mean of 49.9 cm and a standard deviation of 3.74 cm (Ovegard, Berndt & Lunneryd, 2012). Assume the length of fish is normally distributed. Round the probabilities to four decimal places. It is possible with rounding for a probability to be 0.0000. a.) Find the probability that an Atlantic cod has a length that is less than 55.58 cm. b.) Find the probability that an Atlantic cod has a length that is between 40.78 and 55.58 cm. c.) Find the probability that an Atlantic cod has a length that is at least 55.51 cm. d.) Is a length of 55.51 cm unusually long for an Atlantic cod? Why or why not? yes, since the probability of having a length at least that high is less than or equal to 0.05 O yes, since the probability of having a length at the most that value is less than or equal to 0.05 no, since the probability of having a length at least that high is less than or equal to 0.05 O no, since the probability of having a length at the most that value is less than or equal to 0.05 O yes, since the probability of having a length at least that high is greater than 0.05 since the probability of having a length at the most that value is greater than 0.05 yes, no, since the probability of having a length at least that high is greater than 0.05 O no, since the probability of having a length at the most that value is greater than 0.05 e.) What lengths are 68% of all Atlantic cod shorter than? Put an answer rounded to two decimal places in the first box and the correct units in the second box.
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
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![The size of fish is very important to commercial fishing. A study conducted in 2012 found the length of Atlantic cod caught in nets in Karlskrona to have a mean of 49.9 cm and a standard deviation of 3.74 cm (Ovegard, Berndt & Lunneryd, 2012). Assume the length of fish is normally distributed. Round the probabilities to four decimal places. It is possible with rounding for a probability to be 0.0000.
a.) Find the probability that an Atlantic cod has a length that is less than 55.58 cm.
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b.) Find the probability that an Atlantic cod has a length that is between 40.78 and 55.58 cm.
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c.) Find the probability that an Atlantic cod has a length that is at least 55.51 cm.
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d.) Is a length of 55.51 cm unusually long for an Atlantic cod? Why or why not?
- [ ] yes, since the probability of having a length at least that high is less than or equal to 0.05
- [ ] yes, since the probability of having a length at the most that value is less than or equal to 0.05
- [ ] no, since the probability of having a length at least that high is less than or equal to 0.05
- [ ] no, since the probability of having a length at the most that value is less than or equal to 0.05
- [ ] yes, since the probability of having a length at least that high is greater than 0.05
- [ ] yes, since the probability of having a length at the most that value is greater than 0.05
- [ ] no, since the probability of having a length at least that high is greater than 0.05
- [ ] no, since the probability of having a length at the most that value is greater than 0.05
e.) What lengths are 68% of all Atlantic cod shorter than? Put an answer rounded to two decimal places in the first box and the correct units in the second box.
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