Question

6. Assume that x has a normal distribution with the specified mean and standard deviation. Find the following probability:

?(10 ≤ ? ≤ 26); ? = 15, ? = 4 ___________________

7. Find the z-value such that 5.2% of the standard normal curve lies to the left of z.

                                                                 ___________________
   

Answer 1

Answer:

6)

$1590088792230_blob.png$= 15, $1590088792281_blob.png$ = 4

We want to find P( 10 <   < 26 )

T

Where P( 10 <  
T
< 26 ) = P(
T
< 26 ) - P(
T
< 10 )

first find P( < 26 )

T

formula for z-score is

$z=\frac{x - \mu }{\sigma }$

$z=\frac{26- 15 }{4 }$

z = 2.75

P( < 26 ) = P(z < 2.75)

T

using normal z table we get the

P(z < 2.75) = 0.9970

P( < 26 ) = 0.9970

T

now find P( < 10 )

T

formula for z-score is

$z=\frac{x - \mu }{\sigma }$

$z=\frac{10- 15 }{4 }$

z = -1.25

P( < 10 ) = P(z < -1.25)

T

using normal z table we get the

P(z < -1.25) = 0.1056

P( < 10 ) = 0.1056

T

P( 10 <  
T
< 26 ) = P(
T
< 26 ) - P(
T
< 10 )

P( 10 <   < 26 ) =  0.997−0.1056

T

P( 10 <  
T
< 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