At a costumer service call center for a large company, the number of calls received per hour is normally distributed with a mean of 150 calls and a standard deviation of 5 calls. What is the probability that during a given hour of the day there will be between 146 calls and 163 calls, to the nearest thousandth

We have been given that at a customer service call center for a large company, the number of calls received per hour is normally distributed with a mean of 150 calls and a standard deviation of 5 calls. We are asked to find the probability that during a given hour of the day there will be between 146 calls and 163 calls.

First of all, we will use z-score formula to find z-score corresponding to 146 and 163.

Our next step is to find percentage of data scores falls between both z-scores.

Using normal distribution table, we will get:

Let us convert our answer into percentage.

Upon rounding our answer to nearest thousandths, we will get:

Therefore, the probability that during a given hour of the day there will be between 146 calls and 163 calls is approximately .

step-by-step explanation:

f(x)=2x^2 -1 

translation is a function transformation that transform the function in a way of translating. by translating the function its graph is moved  up an down. moving the function f(x) 2 units to the left will be the new function g(x) with the equation: g(x)=f(x+2)=2(x+2)^2 -1