6. Assume that x has a normal distribution with the specified mean and standard deviation. Find the following probability:
?(10 ≤ ? ≤ 26); ? = 15, ? = 4 ___________________
Find the z-value such that 5.2% of the standard normal curve lies to the left of z.
___________________
Answer:
6)
= 15, = 4
We want to find P( 10 < < 26 )
Where P( 10 < < 26 ) = P( < 26 ) - P( < 10 )
first find P( < 26 )
formula for z-score is
z = 2.75
P( < 26 ) = P(z < 2.75)
using normal z table we get the
P(z < 2.75) = 0.9970
P( < 26 ) = 0.9970
now find P( < 10 )
formula for z-score is
z = -1.25
P( < 10 ) = P(z < -1.25)
using normal z table we get the
P(z < -1.25) = 0.1056
P( < 10 ) = 0.1056
P( 10 < < 26 ) = P( < 26 ) - P( < 10 )
P( 10 < < 26 ) = 0.997−0.1056
P( 10 < < 26 ) = 0.8914
7)
We want to find z-score such that the area to the left of z-score is 5.2% = 0.052
now using normal z table find the z-score associated with area 0.052
we get z-score as
Z= -1.6258
rounding to 2 decimals we get
Z = -1.63
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