Question

A pressure sensor provides normally distributed measurements with a mean value of 1,232 mbar. It is known that the standard deviation is 0.048 mbar.

TASK

a)  What is the highest pressure measurement among the 19% lowest pressure measurements? Round your answer to 3 decimal places.

b) What is the lowest pressure measurement among the 9% highest pressure measurements? Round your answer to 3 decimal places.

Answer 1

Solution:-

Given that,

mean = $\mu$ = 1232

standard deviation = $\sigma$ = 0.048

Using standard normal table,

a) P(Z < z) = 19%

= P(Z < z ) = 0.19

= P(Z < - 0.88 ) = 0.19  

z = - 0.88

Using z-score formula,

x = z * $\sigma$ + $\mu$

x = - 0.88 * 0.048 + 1232

x = 1231.958

Using standard normal table,

b) P(Z > z) = 9%

= 1 - P(Z < z) = 0.09  

= P(Z < z) = 1 - 0.09

= P(Z < z ) = 0.91

= P(Z < 1.34 ) = 0.91  

z = 1.34

Using z-score formula,

x = z * $\sigma$ + $\mu$

x = 1.34 * 0.048 + 1232

x = 1232.064