For p(-1.32<Z<1.74) I'd just switch the numbers from negative to positive and vice versa right? Like p(z<1.32) - p (z<-1.74)
No, you cannot simply switch the signs from negative to positive and vice versa when calculating probabilities in this way. The process you are referring to is known as symmetric probability calculations, but it does not apply when you have a range of values.
To calculate the probability for a range of values, such as p(-1.32 < Z < 1.74), you need to use the standard normal distribution table or a statistical software. Here are the steps to calculate this probability:
1. Determine the individual probabilities:
- Calculate p(Z < 1.74): This represents the probability of a standard normal random variable being less than 1.74. You can look up this value in the standard normal distribution table or use a calculator or software.
- Calculate p(Z < -1.32): This represents the probability of a standard normal random variable being less than -1.32. Again, you can refer to the table or use a calculator or software.
2. Calculate the difference between the individual probabilities:
- Subtract p(Z < -1.32) from p(Z < 1.74): p(Z < 1.74) - p(Z < -1.32)
This difference gives you the probability of the standard normal random variable falling within the range -1.32 < Z < 1.74.
Remember, the standard normal distribution table provides the probability of a standard normal random variable being less than a given value (i.e., p(Z < x)). To find the probability between two values, you need to subtract these individual probabilities.