# United States car manufacturers

### Task

Automobile makers need certainly to design the driver’s seat area in order for both high and quick grownups can stay comfortably, attain most of the settings and pedals, and find out through the windshield. Assume a unique car is designed making sure that these conditions are fulfilled for folks from 58 inches to 76 ins high.

The heights of adult men in the us are roughly usually distributed with a suggest of 70 inches and a typical deviation of 3 ins. Heights of adult women can be approximately typically distributed with a mean of 64.5 ins and a regular deviation of 2.5 inches. Just what portion of males in the United States is it automobile maybe not designed to accommodate? Exactly what portion of females in america is this car perhaps not designed to accommodate?

### I am Commentary

This needs students to make use of the normal distribution as a design for a data distribution. Students must use offered means and standard deviations to approximate population percentages.

There are lots of techniques (tables, graphing calculators, or analytical computer software) that students might determine the required normal percentages. With respect to the method utilized, answers might vary notably from those shown in the option.

In issues relating to the regular distribution, encourage pupils to sketch the right normal distribution and shade the location that corresponds into desired probability before using tables or technology to get the likelihood.

### Answer

For men, we want the percentage associated with normal circulation with mean 70 and standard deviation 3 this is certainly above 76 ins or below 58 ins. Since 58 is 4 standard deviations below 70, the percentage below 58 is insignificant, so all we need may be the portion above 76, which corresponds on shaded area into the diagram below. The location with this area is 0.0228, so about 2.3per cent of adult males won’t fit in this vehicle.

For ladies, 76 inches is $\frac{76-64.5}{2.5}=4.6$ standard deviations over the suggest, so essentially 0percent of women are too tall for automobile. Therefore, all we truly need may be the percentage below 58 inches, which corresponds towards the shaded area inside drawing below. The location of the area is 0.00466, therefore about 0.5per cent of adult females won’t easily fit in this automobile.