In Exercises 25–28, find the probabilities and answer the ques...

Question

In Exercises 25–28, find the probabilities and answer the questions.

Too Young to Tat Based on a Harris poll, among adults who regret getting tattoos, 20% say that they were too young when they got their tattoos. Assume that five adults who regret getting tattoos are randomly selected, and find the indicated probability.

d. If we randomly select five adults, is 1 a significantly low number who say that they were too young to get tattoos?

Accepted Answer

Welcome back, everyone. Find the probability and answer the following question. A survey reports that 20% of people who regret buying a certain car model says they made the purchase too late during the model's life cycle. Suppose 5 such individuals are randomly selected. If exactly 1 of them says they bought the car too late, is that number considered significantly low? Now we're essentially asked whether one is a significantly low result out of 5 people, and the value is considered significantly low if the cumulative probability of that value or less is less than or equal to 0.05. No notice that this is a binomial situation because either a person says they bought a car too late or they do not so. If we notice here from our problem that the probability of a two late regret is 0.2 because it's 20%. Which means then that the probability a person would say it's not too late, will be 1 minus 0.2 or 0.8. The number of trials N equals 5 and the value of interest X is equal to 1, then we need to compute the probability that X, let me put that in red here. The probability That X is going to be less than or equal to 1, and that probability would be equal to P 0 plus P 1. OK, the probability is 0 and the probability is 1. These are the only values where X is less than or equal to 1. Know for our binomial situation to find these probabilities we can use the binomial probability formula because no. That means the probability. Of X equals a combination of n and X multiplied by P to the power of X multiplied by 1 minus P or Q to the pore of N minus X. So let's use this to find the probabilities of 0 and 1 and then. We can compare it with the significance threshold to see if it is significantly low. No, that means when X equals 0, for example, the probability of 0 will be equal to 5, the combination of 50 multiplied by 0.2 to the pore of 0 multiplied by Q 0.8 to the pore of 5 minus 0 or 5. When we read that all, that will be 1 multiplied by 1 multiplied by 0.8 to the 5th, which equals 0.32768 or approximately 0.33. On the other hand, When X equals 1, OK, the probability or value will be 1, will be a combination of 5.1 multiplied by 0.2 to the pore of 1, multiplied by 0.8 to the pore of 5 minus 1 or 4. When we work these values out, that's going to be 5 multiplied by 0.2, multiplied by 0.4096, which equals 0.4096, or approximately 0.41. Know that we have these probabilities. That means the probability, so therefore, the probability that X is less than or equal to 1 will be equal to 0.32768, the probability of 0, plus 0.4096, the probability of 1, and that equals 0.73728 or approximately 0.74. Now that we have the value, let's ask ourselves. Is this significantly low? Well, remember, the threshold is 0.05, and since 0.04 is greater than 0.05, that means the value 1. Is not Significantly low. Therefore, we can tell, OK, that our probability that X is less than or equal 1 is 0.74 and that the probability is not significantly low. Thanks a lot for watching everyone. I hope this video helped.

Key Concepts

Binomial Probability

Significance Level

Hypothesis Testing

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