How can I use the normal distribution table to find probabilities other than P(z<Z)?

The normal distribution tables show, for a given Z value, the probability that the random variable z takes a value less than Z or P(z<Z). This is also the area under the normal distribution curve up to Z. We'll call this area A. It is important to remember two things about the normal distribution curve: firstly that the total area under it is 1 and secondly that it is symmetrical.So if we were aiming to find P(z>Z) then we first note that this is the area under the curve from Z upwards. As the sum of the area below Z and above Z must be the total area we see that P(z<Z) + P(z>Z) = 1 and so P(z>Z) = 1-A.In dealing with negative values -Z we use the symmetry of the curve to see that the area below -Z must be equal to the area above Z, giving P(z<-Z) = P(z>Z) = 1-A from the above.Using these two facts we can find the solution to others such as P(z>-Z) or P(m<z<M).

HA
Answered by Holi A. Maths tutor

3737 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How can you tell if a function is even or odd?


Show using mathematical induction that 8^n - 1 is divisible by 7 for n=1,2,3,...


Show that the integral ∫(1-2 sin^2⁡x)/(1+2sinxcosx) dx = (1/2) ln2 between the limits π/4 and 0. [5 marks]


Evaluate the integral (write on whiteboard, too complicated to write here)


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences