517222Question 1/1MandatoryStandardised Random VariableA normally distributed random variable X is converted to Z. Find P(-2<Z<3). (Report the answer as a number rounded to two digits after the decimal point.)

To solve this problem, we need to use the standard normal distribution table, also known as the Z-table. This table gives the probability that a standard normal random variable Z is less than or equal to a given value.

The standard normal distribution has a mean of 0 and a standard deviation of 1. The variable Z in this problem is a standardised version of the original variable X, meaning it has been transformed to have a mean of 0 and a standard deviation of 1.

The problem asks for the probability that Z is between -2 and 3, or P(-2<Z<3).

To find this, we need to find the cumulative probability for Z=3 and Z=-2, and then subtract the two.

Looking up Z=3 in the Z-table, we find a cumulative probability of 0.9987. This means that the probability that Z is less than or equal to 3 is 0.9987.

Looking up Z=-2 in the Z-table, we find a cumulative probability of 0.0228. This means that the probability that Z is less than or equal to -2 is 0.0228.

To find P(-2<Z<3), we subtract the cumulative probability at Z=-2 from the cumulative probability at Z=3:

P(-2<Z<3) = P(Z<3) - P(Z<-2) = 0.9987 - 0.0228 = 0.9759

So, the probability that Z is between -2 and 3 is approximately 0.98 (rounded to two decimal places).