Male players at the high school, college, and professional ranks use a regulation basketball that weighs 22.0 ounces with a standard deviation of 1.2 ounces. Assume that the weights of basketballs are approximately normally distributed. If a basketball is randomly selected, what is the probability that it will weigh between 21.4 and 23.8 ounces

The probability that a basketball will weigh between 21.4 and 23.8 ounces is 0.62465.

Step-by-step explanation:

We have all this information from the question:

To answer this question:

Important concepts to remember:

For this, it is crucial three concepts: the standard normal distribution, the standard normal table, and z-scores:

Roughly speaking, the standard normal distribution is a normal distribution for standardized values. We can obtain standardized values using the formula for z-scores:

[1]

And these values represent the distance from the population mean in standard deviation units. When they are positive, these values are above the population mean, . In case they are negative, they are below .

We can obtain probabilities for any normally distributed data using the standard normal distribution. These values are tabulated into the standard normal table, available in Statistics books or on the Internet.

In general, these values are cumulative probabilities, that is, probabilities from to the value x in question (a raw value).

At this stage, we have enough information to solve the question.

Solving the question

Cumulative probability for ounces.

That is, the raw score is 0.5 standard deviations below, , the population mean.

Since , we can consult the standard normal table, using as an entry (using its first column).

The first row of this table has a second digit in the decimal part for the value of z. In this case, this second digit is zero (or to be more precise, -0.00), because . With the intersection of these two values in the table, namely, -0.5 and -0.00, we finally obtain the cumulative probability, .

Thus,

Cumulative probability for ounces.

We can follow the same steps as before:

using the standard normal table (z =1.5, +0.00).

Therefore,

Then, to answer the probability that a basketball will weigh between 21.4 and 23.8 ounces, we subtract (as we mentioned before) both cumulative probabilities:

Then, the probability that a basketball will weigh between 21.4 and 23.8 ounces is 0.62465.

We can see this probability represented by the shaded area in the below graph.  

answer

false

explanation

these practices describe the manner the land use outcome is attained. land management methods implemented by corporations are a mandatory because they are a driver for better land use results economically, socially and environmentally. corporations are required to understand the connection between land use , and land management practices to support sustainable land use policies

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!