Given that x is a normally distributed random variable with a mean of 50 and a standard deviation of 2, find the probability that x is between 47 and 54.

Let X be the normal variable with mean μ =50 and standard deviation σ =2

We have to find probability that x is between 47 and 54

P(47 < X < 54) = P(X < 54) - P(X < 47)

= -

= P(Z < 2) - P(Z < -1.5)

Using standard normal z score table to find probabilities we get

P(Z < 2) = 0.9772

P(Z < -1.5) = 0.0668

P(47 < X < 54) = P(Z < 2) - P(Z < -1.5)

= 0.9772 - 0.0668

P(47 < X < 54) = 0.9104

The probability that x is between 47 and 54 is 0.9104

steve should create a type of business report called a business plan. the correct option among the options that are already given in the question is the last or the fourth option. this business report created by steve will actually influence the investors about investing their money in steve's business. this business report will have all the details about the business, the amount of investment required and the amount of expected profit.