no 32
a the distribution of the sample mean will be a normal distribution
b standard error of the mean
= 8/4
= 2
c P(x>140)
=
=
= P ( z > 2.5)
= 0.4938
= 0.5 - 0.4938
= 0.0062
d P(x>128)
=
=
=
= P ( z < 3.5)
= 0.5
= 0.5 + 0.5
= 1
e P ( 128 < X < 140)
=
P ( z > -3.5)
𝜎
𝑛 = 8
16
𝑃(𝑥 − 𝜇 𝜎
𝑛
> 140 − 𝜇 𝜎
𝑛 )
𝑃( 𝑧 > 140 − 135 8 16
)
𝑃( 𝑧 > 5 2)
𝑃(𝑥 − 𝜇 𝜎
𝑛
> 128 − 𝜇 𝜎
𝑛 )
𝑃( 𝑧 > 128 − 135 8 16
)
𝑃( 𝑧 > −7 2 )
𝑃( 128 − 𝜇 𝜎
𝑛
< 𝑥 − 𝜇 𝜎
𝑛
< 140 − 𝜇 𝜎
𝑛 )
𝑃( 128 − 135 8 16
< 𝑧 < 140 − 135 8 16
)
=
=
= 0.5 + 0.4938
= 0.9938
P ( -3.5 < z < 2.5) 𝑃(−7
2 < 𝑧 < 5 2)
16 16
https://www.slader.com/discussion/question/cra-cds-inc-wants-the-mean-lengths-of-the-cuts-on-a-cd-to-be-135-secondsthis-will-allow-the-disk-joc/#:~:text=CRA%20CDs%20Inc.-,wants%20the%20mean%20lengths%20of%20the%20%E2%80%9Ccuts%E2%80%9D%20on%20a%20CD,within%20each%2010%2Dminute%20segment.
https://www.slader.com/discussion/question/cra-cds-inc-wants-the-mean-lengths-of-the-cuts-on-a-cd-to-be-135-secondsthis-will-allow-the-disk-joc/#:~:text=CRA%20CDs%20Inc.-,wants%20the%20mean%20lengths%20of%20the%20%E2%80%9Ccuts%E2%80%9D%20on%20a%20CD,within%20each%2010%2Dminute%20segment.
https://www.slader.com/discussion/question/cra-cds-inc-wants-the-mean-lengths-of-the-cuts-on-a-cd-to-be-135-secondsthis-will-allow-the-disk-joc/#:~:text=CRA%20CDs%20Inc.-,wants%20the%20mean%20lengths%20of%20the%20%E2%80%9Ccuts%E2%80%9D%20on%20a%20CD,within%20each%2010%2Dminute%20segment.
https://www.slader.com/discussion/question/cra-cds-inc-wants-the-mean-lengths-of-the-cuts-on-a-cd-to-be-135-secondsthis-will-allow-the-disk-joc/#:~:text=CRA%20CDs%20Inc.-,wants%20the%20mean%20lengths%20of%20the%20%E2%80%9Ccuts%E2%80%9D%20on%20a%20CD,within%20each%2010%2Dminute%20segment.
