Mathematics: Aset of mugs costs $21.50. the sales-tax rate is 4.5 percent. what is the total amount you need to pay? you can use either method. $3.17 $22.47 $96.75

Aset of mugs costs $21.50. the sales-tax rate is

laceytoyne72

09.02.2021

(a) Shown below

(b) The expected time it takes for the bus to arrive is 7.5 minutes.

Step-by-step explanation:

Let X = waiting time for the bus.

It is provided that the bus arrives at the bus stop uniformly between 9:05 AM and 9:10 AM.

The random variable X is uniformly distributed with parameters a = 5 and b = 10.

The probability density function of a Uniform distribution is:

$f_{X}(x)=\frac{1}{b-a};\ a$

(a)

The probability density function of the random variable X is:

$f_{X}(x)=\left \{ {{\frac{1}{10-5};\ a$

The cumulative distribution function of the random variable X is:

$=0;\ for\ x$

$F_{X}(x)=\frac{x-a}{b-a}=\frac{x-5}{10-5};\ x\epsilon[a, b]$

$=1;\ for\ xb$

(b)

The expected value of Uniform distribution is:

$E(X)=\frac{1}{2}(a+b)$

Compute the expected value of X as follows:

$E(X)=\frac{1}{2}(a+b)$

$=\frac{1}{2}\times (5+10)$

$=\frac{1}{2}\times 15$

=7.5

Thus, the expected time it takes for the bus to arrive is 7.5 minutes.

(c)

If I reach the bus stop at 9:07 AM and I have missed the bus, then this implies that the bus arrived between 9:05 AM and 9:07 AM.

Compute the probability that the bus arrived between 9:05 AM and 9:07 AM as follows:

P(5

$=\frac{1}{5}\times \int\limits^{7}_{5}{1}\, dx$

$=\frac{1}{5}\times |x|^{7}_{5}$

$=\frac{1}{5}\times (7-5)$

$=\frac{1}{5}\times 2\\$

=0.40

Thus, the probability that the bus was missed if I arrived at the bus stop at 9:07 AM is 0.40.

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