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2 sf standard normal distribution table

For example, if X follows a standard normal distribution,, what is the probability of P(X<=0.145) by using the above table only? Is it possible to tell? I remember I once encounter this situation in an exam long time ago, but I don't have a definite solution for this.

Certainly, P(X<=0.145) should be between P(X<=0.14) and P(X<=0.15) which can be obtained from the table directly without a doubt. It will be tempted to say P(x<=0.145) = [P(X<=0.14)+P(X<=0.15)]/2 which is what I did in that exam. However, I don't think it is correct.

Ken T
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  • Please add the `[self-study]` tag & read its [wiki](http://stats.stackexchange.com/tags/self-study/info). Then tell us what you understand thus far, what you've tried & where you're stuck. We'll provide hints to help you get unstuck. – gung - Reinstate Monica Feb 16 '17 at 13:19
  • The table you show already works to three figures as indicated at the linked question (i.e. the value for the area to the left of 1.45 is in the table already); you would use interpolation to approximate a fourth significant figure. – Glen_b Feb 16 '17 at 15:56
  • Also see the diagram [here](http://stats.stackexchange.com/questions/252645/calculate-p-value-for-a-negative-z) which illustrates how to use this sort of table – Glen_b Feb 16 '17 at 16:03
  • @Glen_b Very good reference!!! But any discussion on why the linear / log / logit/ inverse interpolation will work? – Ken T Feb 16 '17 at 16:59
  • Linear interpolation works because when you zoom right into a smooth function it's approximately linear. Since tables tend to be fine-grained, they're approximately linear between steps. There's an extended discussion of the mechanics of linear and nonlinear interpolation linked in an answer under the indicated duplicate at the top. If you want more detail than that you will need a new question – Glen_b Feb 17 '17 at 00:44

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