The pressure inside a stabilizing component in a spacecraft is normally distribu

Question

The pressure inside a stabilizing component in a spacecraft is normally distributed with mean 120 and standard deviation 10. a) What is the probability that the pressure is less than 100? b) What is the probability that the pressure is between 123 and 127? c) In order to maintain communication and control a short circuit load center is designed to kick in when the pressure crosses a certain threshold value. Typically in civilian applications, the threshold region is in the top 10%. What is the value of this threshold?

Explanation / Answer

Solution:-

a). Since = 120 and = 10 we have:

P ( X < 100 ) = P ( X < 100 120 ) = P ((X)/ < (100120)/10)

Since (x)/ = Z and (100120)/10 = 2, we have:

P (X < 100) = P (Z < 2)

Using the standard normal table to conclude that:

P (Z < 2) = 0.0228

b).

Since = 120 and = 10 we have:

P ( 123 < X < 127 ) = P ( 123120 < X < 127120 ) = P ( (123120)/10 < (X)/ < (127120)/10)

Since Z=(x)/ ,

(123120)/10 = 0.3 and (127120)/10 = 0.7 we have:

P ( 123 < X < 127 ) = P ( 0.3 < Z < 0.7 )

Using the standard normal table to conclude that:

P ( 0.3 < Z < 0.7 ) = 0.1401

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