One piece of pvc pipe is to be inserted inside another piece. the length of the first piece is normally distributed with mean value 20 in. and standard deviation .5 in. the length of the second piece is a normal rv with mean and standard deviation 15 in. and .4 in., respectively. the amount of overlap is normally distributed with mean value 1 in. and standard deviation .1 in. assuming that the lengths and amount of overlap are independent of one another, what is the probability that the total length after insertion is between 34.5 in. and 35 in.?

0.159 is the probability that the total length after insertion is between 34.5 inch and 35 inch.  

Step-by-step explanation:

We are given the following information in the question:

The length of the first piece is normally distributed with mean value 20 inch and standard deviation 0.5 inch.

The length of the second piece is a normal with mean and standard deviation 15 inch  and 0.4 inch respectively.

The amount of overlap is normally distributed with mean value 1 inch and standard deviation 0.1 inch.

The lengths and amount of overlap are independent of one another.

Let the total length of PVC pipe be represented by Y.

The sum of two independent normally distributed random variables is normal, with its mean being the sum of the two means, and its variance being the sum of the two variances

Then, Y follows a normal distribution with

Y = Length of first pipe + Length of second Pipe - Overlap

P(total length after insertion is between 34.5 inch and 35 inch)

0.159 is the probability that the total length after insertion is between 34.5 inch and 35 inch.  

boxplot e is the answer

"it's not the heat, it's the humidity".   that's a partly valid phrase you may have heard in the summer, but it's actually both.   the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature.   this has important considerations for the human body's comfort.   when the body gets too hot, it begins to perspire or sweat to cool itself off.   if the perspiration is not able to evaporate, the body cannot regulate its temperature.   evaporation is a cooling process.   when perspiration is evaporated off the body, it effectively reduces the body's temperature.   when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases.   in other words, the human body feels warmer in humid conditions.   the opposite is true when the relative humidity decreases because the rate of perspiration increases.   the body actually feels cooler in arid conditions.   there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

step-by-step explanation: