Monthly sales are independent normal random variables with mean 100 and standard deviation 5. (a) find the probability that exactly 3 of the next 6 months have sales greater than 100. (b) find the probability that the total of the sales in the next 4 months is greater than 420

The probability that exactly 3 of the next 6 months have sales greater than 100 is 0.31 and the probability that the total of the sales in the next 4 months is greater than 420 is 0.42.

Given :

Monthly sales are independent normal random variables with a mean of 100 and a standard deviation of 5.

The probability is given by the formula:

a) The probability that exactly 3 of the next 6 months have sales greater than 100 is given by:

b) The probability that the total of the sales in the next 4 months is greater than 420 is given by:

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Let be the random variable for the value of goods sold in any given month. Also let be the random variable representing the number of times that sales in a given month surpass a value of 100.

follows a normal distribution with mean and standard deviation , while would follow a binomial distribution with some success probability on trials. To find , we use the distribution of :

where is a random variable following the standard normal distribution.

a) The probability that exactly 3 of the next 6 months have sales greater than 100 is then

b) Let be the random variable representing the total value of sales over 4 months, and denote by the random variable for the value of sales during month . Then , and we want to find .

We know the are mutually independent and identically distributed, and we (you probably should, anyway) also know that the sum of i.i.d. normally distributed random variables also follows a normal distribution, whose mean is the sum of the means, and whose standard deviation is the sum of the squares of the standard deviations, of the i.i.d. random variables:

Then the probability we want is

If the distance between two charged objects increases then the strength of the electrical force between the objects decreases.

Step-by-step explanation:

If the distance between two charged objects increases then by Coulomb's law, there is an inverse relation between the force and the square of the distance.

Thus, the strength of the electrical force between the objects decreases.

Coulomb's law tells that a force proportional to the product of the charges and inversely proportional to the square of the distance between them.

It also tells that like charges repel and opposite charges attract .