Question

In: Statistics and Probability

(a) Find ​P(T<1.321) when v=22. ​(b) Find ​P(T>2.069​) when v=23. ​(c) Find ​P(−2.145<T<2.997​) when v=14. ​(d)...

(a) Find ​P(T<1.321) when v=22. ​(b) Find ​P(T>2.069​) when v=23. ​(c) Find ​P(−2.145<T<2.997​) when v=14. ​(d) Find ​P(T>−2.998) when v=7.

Solutions

Expert Solution

We use the Excel function T.DIST to find the probabilities

a)   P(T < 1.321) = T.DIST(1.321, 22, TRUE)        (Given degrees of freedom, v = 22)

    P(T < 1.321) = 0.89996

b)   ​P(T>2.069​) = 1 - P(T < 2.069)                        (Given degrees of freedom, v = 23)

                          = 1 - T.DIST(2.069, 23, TRUE)

                          = 0.02498

       P(T>2.069​)  = 0.02498

c)  ​P(−2.145 < T < 2.997​)                          (Given degrees of freedom, v = 14)

      ​P(−2.145 < T < 2.997​) = P(T < 2.997) - P(T < -2.145)

                                      = T.DIST(2.997, 14, TRUE) - T.DIST(-2.145, 14, TRUE)

                                      = 0.995196 - 0.02499

                                       = 0.97021

     ​P(−2.145 < T < 2.997​) = 0.97021

d)   P(T > −2.998) = 1 - P(T < -2.998)                              Given degrees of freedom, v = 7

                              = 1 - T.DIST(-2.998, 7, TRUE)

                              = 1 - 0.00999

                              = 0.990001

      P(T > −2.998) = 0.990001

       

orchestra answered 1 year ago
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