A large sample of tires from cabs driven within a city have an average tire tread depth of 0.25cm at the end of the winter. If the city’s average winter tire tread depth is 2.2cm, with a standard deviation of 0.33cm at the end of the same winter, what is the probability cab tires depths would be shallower than 0.25cm.

0% probability cab tires depths would be shallower than 0.25cm.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

What is the probability cab tires depths would be shallower than 0.25cm.

This probability is the pvalue of Z when X = 0.25. So

has a pvalue of 0.

0% probability cab tires depths would be shallower than 0.25cm.

A function is a relationship that maps elements from a set (the domain) into elements from another set (the range)

Such that each element in the domain can be mapped into only one element from the range.

Let's see graphs 18, 20,24 and 30.

Remember that the axis that represents the domain is the horizontal one (usually represented with x), and the vertical axis represents the range (usually represented with y)

18) Here we can see that the point x = 1 his mapped into two different values of y.

we have the pair (1, 2) and the pair (1, -3)

And something similar happens for x = 2.

Then we can conclude that this is not a function.

20) Here we have a linear relationship.

Linear relationships are almost always functions, the only case when these are not functions is when the linear equation is something like x = a.

Linear equations can be written as:

y = a*x + b

So x can be any value, and thus y also can be any value.

Then the domain is the set of all real numbers, and the range is the set of all real numbers.

24) Here we have a quadratic function whose arms go down.

This is a function, now let's see the domain and range.

Quadratic functions are written as:

y = a*x^2 + b*x + c

There is no value of x can cause some problem in this equation, then this function works for all values of x, then the domain is the set of all real numbers.

Now, let's look at the graph.

We can see that the function goes up, reaches a maximum, and then goes down again.

Then the range will be the set of all the values smaller than the maximum we can see in the graph, this is:

y ∈ (-∞, 15]

or simply:

y ≤ 15.

30) Here again, we can see that for x = 0 there are two different values of y.

the same happens for x = -1, x = -2, and a lot of other values.

Then this is not a function, because it is mapping values of the domain into different values of the range.