A data sample consists of 50 measurements of pressure. The sample has a mean val

Question

A data sample consists of 50 measurements of pressure. The sample has a mean value of 1.20 in. H2O and a standard deviation of 0.11 in. H2O. Assume the data are normally distributed. Over a range of pressures from 1.08 in. H2O to 1.55 in. H2O, consider the following:

i) Determine the probability that the pressure measurements will lie within the given range.

ii) Calculate the number of pressure measurements expected to lie within the given range (to the nearest whole number).

*** I understand how to find the Z values. I end up getting P(-1.09 < z < 3.18). But using these values I am not sure how to find P(z1) and P(z2). The answers should be 0.3643 and 0.4996, but I have no idea how to get to them beause my solutions don't explain it. I know how to do the rest of the problem. I only need help with this portion.***

Thank You

Explanation / Answer

Solution:

i) From the given information Mean = 1.20 and Standard deviation = 0.11
n = 50
P( 1.08 < X < 1.55 ) = P(1.081.2/0.11< X/ < 1.551.2/0.11)
= P(1.09 < Z < 3.18 )
= P ( Z < 3.18 )P (Z < 1.09 )
= 0.9993 - 0.1379
= 0.8614

ii) number of pressure measurements expected to lie within the given range
  
np = 50 * 0.8614
= 43.07

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