Weekly wages at a certain factory are normally distributed with a mean of $400 and a standard deviation of 50$. find the probability that a worker selected at random makes between $350 and $400.

.34 or 34%

Step-by-step explanation:

You should probably draw and label a normal distribution curve to help you visualize the problem.

The mean is in the middle and is where you start from. Normal distribution curves go out 3 standard deviations from the mean, and the standard deviation you are given is 50.

Therefore, 1 standard deviation under/below the mean would be 400 - 50 = 350.

Standard deviations have a set percentage/probability from the mean. I'm sure you've heard of the 68-95-99.7 rule? One standard deviation from the mean is 68%, but since you only want one standard deviation under the mean, you can divide by 2 to get 34%.

So there is a 34% chance that a worker selected at random makes between $350-$400.

2 ( Option A )

Step-by-step explanation:

The given integral to us is ,

Here 5 is a constant so it can come out . So that,

Now we can write √x as ,

Simplify ,

By Power rule , the integral of x^3/2 wrt x is , 2/5x^5/2 . Therefore ,

On simplifying we will get ,