Colder then -7.2 F would be -8.5 F

-7.2 > -8.5

anything to the left of -7.2 on the number line will be less then(oe in this case, colder then) -7.2....so -8.5 falls to the left of -7.2

8 0

3 years ago

Suppose that the probability density function ofthe length of computer cables is f (x) = 0.1 from 1200 to1210 millimeters.a. Det

Ann [662]

Notice that $f(x)=0.1$ for $1200\le x\le1210$ implies that $f(x)=0$ elsewhere, since

$\displaystyle\int_{1200}^{1210}f(x)\,\mathrm dx=1$

where $X=x$ is a random variable representing cable lengths according to the PDF $f(x)$ .

a. By definition of expectation, the mean is

$E[X]=\displaystyle\int_{-\infty}^\infty x\,f(x)\,\mathrm dx=0.1\int_{1200}^{1210}x\,\mathrm dx=1205$

The variance is

$\operatorname{Var}[X]=E[(X-E[X])^2]=E[X^2]-E[X]^2$

where

$E[X^2]=\displaystyle\int_{-\infty}^\infty x^2\,f(x)\,\mathrm dx=0.1\int_{1200}^{1210}x^2\,\mathrm dx=\frac{4,356,100}3$

so that the variance is $\frac{25}3$ , making the standard deviation $\frac5{\sqrt3}$ .

b. The proportion of cables within specs is

$P(1195$

8 0

4 years ago