1) A TV manufacturer offers a \(10\) year warranty. Research has shown that their TVs last an average of \(12\) years, with a standard deviation of \(2\) years.
a) Estimate the probability that a TV will fail during the warranty period.
b) Estimate the probability that a TV will last at least \(16\) years.
c) Estimate the probability that a TV will last less than \(6\) years.
d) Estimate the probability that a TV will have a lifetime between \(6\) and \(14\) years.
2) Use your Left Tail Z-Table and round answers to the nearest hundredth or hundredth of a percent. A new battery operated car averages \(250\) mpg on the highway with a standard deviation of \(50\) mpg. Assuming that the distribution is normal, find the probability that a new car of this model will get between \(117\) and \(312\) mph.
3) Use your Calculator and sketch the normal curve and label or shade the problem accordingly. Round raw values to the nearest hundredth or probabilities to the nearest hundredth of a percent. The ages of people who went skydiving on a random day during the summer are normally distributed with a mean of \(36\) years old and a standard deviation of \(6\) years. Calculate the probability that a person is at least \(50\) years old.
4) Scores on the IQ Test are normally distributed with a mean of \(100\) and a standard deviation of \(15\). Scores on the CogAT test are normally distributed with a mean of \(101\) and a standard deviation of \(13\). Note: IQ/CogAT test scores must be rounded to the nearest integer. Use your calculator to answer the following problems:
a) If a person scores in the \(90th\)percentile (Note: percentile means the person scored better than \(90\%\) of those taking
the test), find the actual IQ score and an equivalent CogAT score.
b) Find the equivalent CogAT score for an IQ Test score of \(140\).
5) The age at which babies talk is normally distributed. \(10\%\) of babies say their first word by \(9\) months and \(95\%\) of babies have said their first word by \(18\) months. Use a calculator to find the mean and the SD to the nearest thousandth.
Solution Bank
a) Estimate the probability that a TV will fail during the warranty period.
b) Estimate the probability that a TV will last at least \(16\) years.
c) Estimate the probability that a TV will last less than \(6\) years.
d) Estimate the probability that a TV will have a lifetime between \(6\) and \(14\) years.
2) Use your Left Tail Z-Table and round answers to the nearest hundredth or hundredth of a percent. A new battery operated car averages \(250\) mpg on the highway with a standard deviation of \(50\) mpg. Assuming that the distribution is normal, find the probability that a new car of this model will get between \(117\) and \(312\) mph.
3) Use your Calculator and sketch the normal curve and label or shade the problem accordingly. Round raw values to the nearest hundredth or probabilities to the nearest hundredth of a percent. The ages of people who went skydiving on a random day during the summer are normally distributed with a mean of \(36\) years old and a standard deviation of \(6\) years. Calculate the probability that a person is at least \(50\) years old.
4) Scores on the IQ Test are normally distributed with a mean of \(100\) and a standard deviation of \(15\). Scores on the CogAT test are normally distributed with a mean of \(101\) and a standard deviation of \(13\). Note: IQ/CogAT test scores must be rounded to the nearest integer. Use your calculator to answer the following problems:
a) If a person scores in the \(90th\)percentile (Note: percentile means the person scored better than \(90\%\) of those taking
the test), find the actual IQ score and an equivalent CogAT score.
b) Find the equivalent CogAT score for an IQ Test score of \(140\).
5) The age at which babies talk is normally distributed. \(10\%\) of babies say their first word by \(9\) months and \(95\%\) of babies have said their first word by \(18\) months. Use a calculator to find the mean and the SD to the nearest thousandth.
Solution Bank