Answer on Statistics and Probability Question for bx
a) Find the probability that the strength is less than 8200 kg per sq. cm
b) Find the probability that the strength is between 7500 and 7700 kg per sq. cm
c) Determine the value for which the probability that the strength of cement is below this value is 90%.
Then Z = (X-8000)/200 has standard normal distribution.
a) P(X<8200) =
& = P( (X-8000)/200 < (8200-8000)/200 )=
= P(Z<1)= 0.841345
& b) P(7500 < X< 7700)& = P( (7500-8000)/200 <Z< (7700-8000)/200 )=
P( -2.5<Z< -1.5 )= F(-1.5)-F(-2.5)= F(2.5)-F(1.5)=
= 0.99379 - 0,933193 = 0.060598
c) We have to find such& S& that
P(X<S) = 0.9
0.9 = P(X<S) = P(Z < (S-8000)/200 ) =
Then, using known values of F we obtain that
(S-8000)/200 = 1.281552
Hence S = 1.281552*200+8000=8256.31
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