P68: This means we need to find the value on the normal distribution curve that has 68% of the area under the curve to its left. Therefore, the value on the normal curve at P32 is: Using a standard normal distribution table, we find that the z-score corresponding to P32 is approximately -0.44. P32: This means we need to find the value on the normal distribution curve that has 32% of the area under the curve to its left. Therefore, the value on the normal curve at P90 is: Using a standard normal distribution table, we find that the z-score corresponding to P90 is approximately 1.28.

P90: This means we need to find the value on the normal distribution curve that has 90% of the area under the curve to its left. We are looking for above 2.24, and this gives us our answer. We know the mean = 0, standard deviation = 1, since we are dealing with a standard normal distribution (that is what a Z score uses). You could also use an online calculator like this one: The second solution would be to use a command on your calculator, such as a TI-84. This gives us the same answer if we look at our table. Alternatively, with this method, since we know a normal distribution is symmetric, the P(Z≤-2.24) = P(Z>2.24), which we can find using the table as well. Since we are concerned with what is greater than 2.24, we subtract this value from 1. We find that the probability that Z ≤ 2.24 = 0.98745. Here is a good one: įirst, we find the Z-score of interest.

The first way, and probably the way they want you to solve this, is using a Z-score table. So, since we know that, for a normal distribution, area = probability, what this question is asking is - what is probability that we get a Z-score greater than 2.24? Aka: in a standard normal distribution, what is the area from 2.24 to infinity? This means that the distribution itself represents the probability of getting something (since the area under the entire curve is 1). :)Īll a Z-score is is a certain 'cutoff point' on a standard normal distribution - this is a normal distribution with mean 0 and standard deviation 1. All of the questions you posted use the exact same ideology, so I'll answer one, and you can message me if you need help with the others.

Standard normal table z score P90