The mean weight of loads of rock is 42.0 tons with a standard deviation of 12.0 tons. if 25 loads are chosen at random for a weight check, find the probability that the mean weight of those loads is less than 40.7 tons. assume that the variable is normally distributed.

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the weigths of rock from population, and for this case we know the distribution for X is given by:

Where and

The distribution for the sample mean is given by:

For this case we want to find this probability:

And for this we can use the z score given by:

And if we use this formula we got:

And if we use the normal standard table or excel we find the probability:

the equation cos(35) =a/25 can be used to find the length of bc what is the length of bc? round to the nearest tenth

step-by-step explanation:

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step-by-step explanation: