Question

1. Sketch the area under the standard normal curve over the indicated interval and find the specified area. (Round your answer to four decimal places.)

The area to the right of z = 1.50 is _________

2. Sketch the area under the standard normal curve over the indicated interval and find the specified area. (Round your answer to four decimal places.)

The area to the left of  z = −1.33  is ________

3. Sketch the area under the standard normal curve over the indicated interval and find the specified area. (Round your answer to four decimal places.)

The area between  z = −2.25 and z = 1.41 is ________

4.Sketch the area under the standard normal curve over the indicated interval and find the specified area. (Round your answer to four decimal places.)

The area between z = −2.48 and z = −1.80 is ________

5. Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)

μ = 5.0; σ = 2.4.

P(3 ≤ x ≤ 6) = ________

6. Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)

μ = 109; σ = 12

P(x ≥ 90) = ________

Answer 1

1)

= P(Z ≥   1.500   ) = P( Z <   -1.500   ) =    0.0668   (answer)

2)

=P(Z ≤   -1.330   ) =   0.0918   (answer)

3)

P (    -2.250   < Z <    1.410   )                       
= P ( Z <    1.410   ) - P ( Z <   -2.250   ) =    0.9207   -    0.0122   =    0.9085   (answer)

4)

P (    -2.480   < Z <    -1.800   )                           
= P ( Z <    -1.800   ) - P ( Z <   -2.480   ) =    0.0359   -    0.0066   =    0.0294   (answer)  

5)

µ =    5                                  
σ =    2.4                                  
we need to calculate probability for ,                                      
P (   3   < X <   6   )                      
=P( (3-5)/2.4 < (X-µ)/σ < (6-5)/2.4 )                                      
                                      
P (    -0.833   < Z <    0.417   )                       
= P ( Z <    0.417   ) - P ( Z <   -0.833   ) =    0.6615   -    0.2023   =    0.4592   (answer)

6)

µ =    109                      
σ =    12                      
                          
P ( X ≥   90   ) = P( (X-µ)/σ ≥ (90-109) / 12)                  
= P(Z ≥   -1.583   ) = P( Z <   1.583   ) =    0.9433   (answer)  
excel formula for probability from z score is =NORMSDIST(Z)