1. (b) What proportion of the population would have IQ above 115? (express as a decimal, to 3 decimal places)

IQ scores are normally distributed with mean 100 and standard deviation 15.1. (b) What proportion of the population would have IQ above 115? (express as a decimal, to 3 decimal places)

IQ scores are normally distributed with mean 100 and standard deviation 15.2. What proportion of the population would have IQ above Marvin's score of 146? (express as a decimal, to 3 decimal places)

Part B.We tend to prize intelligence very highly, especially the kind of logical reasoning ability that is used a lot in QM1 and that can be measured using IQ tests. IQ tests are designed so that scores across the general public are normally distributed with mean 100 and standard deviation 15.(If you feel like trying a simple informal IQ test, just Google "online IQ test" and take your pick!)Suppose you score 115 on an IQ test. Where does that place your intelligence relative to the general public? Specifically:(a) what proportion of the population would be below 115?(b) what proportion of the population would be above 115?The ultimate in IQ is MarvinLinks to an external site. , who has "a brain the size of a planet". His IQ is astronomical, but for our purposes let's say it is 146. Where is Marvin's IQ placed relative to the general population.(Clearly Marvin is not very happy. In fact he spends a lot of time feeling very depressed. His astronomical IQ is not enough to make him happy.)Research has suggested that IQ alone may not be sufficient for a happy successful life. Angela Duckworth has led research suggesting that "grit" may be as important as IQ! Grit is "perseverance and passion in the pursuit of long term goals" and, as part of the research, a "grit scale" was developed.(You can meet Angela Duckworth hereLinks to an external site.... about 6 minutes, not necessary for the tutorial, but you may find it interesting. You can estimate your own grit hereLinks to an external site..)Grit scores are continuous between 0 and 5, with higher scores indicating greater grittiness. The percentiles of the distribution in the general population are given in the following table.Percentile Male Female10 2.51 2.5120 2.83 2.8830 3.06 3.1340 3.25 3.2550 3.38 3.5060 3.54 3.6370 3.75 3.7980 3.92 4.0090 4.21 4.25100 5.00 5.00(a) What are the median grit scores for males and females?(b) If Marvin is the ultimate in IQ, then the ultimate in grit is RickLinks to an external site.... he is never going to give you up! Rick scored 4.21 on the grit scale. Where does this place his grittiness relative to the general population?

Suppose one individual is randomly chosen. Find the probability that this person has an IQ less than 125.Write your answer in percent form. Round to the nearest tenth of a percent.P𝑃 (IQ less than 125) =

According to the normal distribution of IQ scores (with a mean of 100 and standard deviation of 15), what percentage of the test takers will get scores between 85 and 115? 16 32 34 68