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Mary conducted a study to investigate whether first year science students were more likely than University students in general to use laptops (or tablets) to take notes in lectures. Within the population of university students only 20% reported that they used laptops or tablets to take notes in lectures. A random sample of 40 first year science students was selected and it was found that 14 students reported using laptops or tablets to take notes in lectures.Mary assumed first year science students were no different from University students in general with regards to their use of laptops (tablets) in lectures.   She then used a normal approximation to determine the probability of observing 14 or more students, out of 40, using laptops (tablets). Which one of the following statements is false?   If she didn't use a continuity correction her probability will be an underestimate of the exact probability  If she did use a continuity correction her probability will still be an underestimate of the exact probability   Assuming Mary's model is correct, the exact probability of observing 14 students  using a laptop or tablet to take notes in lectures is 0.0115  If Mary repeated this study many times then approxiately 14 times out of 1000  she should expect to observe 14 or more first year science students using a laptop or tablet (to take notes in lectures).   Based on evidence form Mary's sample,  first year science students seem to be more likley to use laptops (tablets) in lectures than the university students in general.Revise the end of chapter 4 - normal approximation to the Binomial. Also have a play with the applet to help clarify. If you find this really difficult to do intuitively, then you can just calculate the exact and approximate probabilities using Minitab. Question 91 / 1 ptsWhich one of the following  is likely to be well described by a Binomial model?  The number of accidents in a large factory during one 8-hour shift   The number of spades in a bridge hand (ie a random selection of 13 cards from a pack of 52 cards)   The number of tosses of a fair coin until the 10th head is obtained   The number of years between floods at a certain location   The number of apples that are 'infected' in a sample of 40 apples randomly selected from a large consignment of apples.

Question

Mary conducted a study to investigate whether first year science students were more likely than University students in general to use laptops (or tablets) to take notes in lectures. Within the population of university students only 20% reported that they used laptops or tablets to take notes in lectures. A random sample of 40 first year science students was selected and it was found that 14 students reported using laptops or tablets to take notes in lectures.Mary assumed first year science students were no different from University students in general with regards to their use of laptops (tablets) in lectures.   She then used a normal approximation to determine the probability of observing 14 or more students, out of 40, using laptops (tablets). Which one of the following statements is false?   If she didn't use a continuity correction her probability will be an underestimate of the exact probability  If she did use a continuity correction her probability will still be an underestimate of the exact probability   Assuming Mary's model is correct, the exact probability of observing 14 students  using a laptop or tablet to take notes in lectures is 0.0115  If Mary repeated this study many times then approxiately 14 times out of 1000  she should expect to observe 14 or more first year science students using a laptop or tablet (to take notes in lectures).   Based on evidence form Mary's sample,  first year science students seem to be more likley to use laptops (tablets) in lectures than the university students in general.Revise the end of chapter 4 - normal approximation to the Binomial. Also have a play with the applet to help clarify. If you find this really difficult to do intuitively, then you can just calculate the exact and approximate probabilities using Minitab. Question 91 / 1 ptsWhich one of the following  is likely to be well described by a Binomial model?  The number of accidents in a large factory during one 8-hour shift   The number of spades in a bridge hand (ie a random selection of 13 cards from a pack of 52 cards)   The number of tosses of a fair coin until the 10th head is obtained   The number of years between floods at a certain location   The number of apples that are 'infected' in a sample of 40 apples randomly selected from a large consignment of apples.

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Solution

The question asks which of the following scenarios is likely to be well described by a Binomial model. Let's evaluate each option:

  1. The number of accidents in a large factory during one 8-hour shift - This is not a binomial scenario because the number of trials (working hours or workers) is not fixed and the probability of an accident occurring is not constant.

  2. The number of spades in a bridge hand (i.e., a random selection of 13 cards from a pack of 52 cards) - This is not a binomial scenario because the trials (card draws) are not independent. Once a card is drawn, it is not replaced, changing the probabilities for subsequent draws.

  3. The number of tosses of a fair coin until the 10th head is obtained - This is not a binomial scenario because the number of trials is not fixed. It continues until a certain condition (10 heads) is met.

  4. The number of years between floods at a certain location - This is not a binomial scenario because the trials (years) are not independent. The probability of a flood in a given year may depend on whether there was a flood in the previous year.

  5. The number of apples that are 'infected' in a sample of 40 apples randomly selected from a large consignment of apples - This is a binomial scenario. The trials (apples) are independent, the number of trials is fixed (40), and the probability of success (an apple being infected) is the same for each trial.

Therefore, the statement "The number of apples that are 'infected' in a sample of 40 apples randomly selected from a large consignment of apples." is likely to be well described by a Binomial model.

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