1)
a)
µ = 9
σ = 5
P( X ≤ 19 ) = P( (X-µ)/σ ≤ (19-9)
/5)
=P(Z ≤ 2.000 ) =
0.9772 (answer)
b)
µ = 9
σ = 5
P ( X > 4 ) = P( (X-µ)/σ ≥ (4-9) / 5)
= P(Z ≥ -1.000 ) = P( Z <
1.000 ) = 0.8413
(answer)
========================
2)
a)
µ = 60
σ = 18
P ( X > 98 ) = P( (X-µ)/σ ≥ (98-60) /
18)
= P(Z ≥ 2.111 ) = P( Z <
-2.111 ) = 0.0174
(answer)
b)
P( X < 85 ) = P( (X-µ)/σ ≤ (85-60)
/18)
=P(Z ≤ 1.389 ) =
0.9176 (answer)
=====================
3.1)
µ = 11.3
σ = 2.6
P ( X ≥ 13 ) = P( (X-µ)/σ ≥ (13-11.3) /
2.6)
= P(Z ≥ 0.654 ) = P( Z <
-0.654 ) = 0.2566
(answer)
3.2)
P( X ≤ 13 ) = P( (X-µ)/σ ≤ (13-11.3)
/2.6)
=P(Z ≤ 0.654 ) =
0.7434 (answer)
3.3)
we need to calculate probability for ,
P ( 11 < X <
12 )
=P( (11-11.3)/2.6 < (X-µ)/σ < (12-11.3)/2.6 )
P ( -0.115 < Z <
0.269 )
= P ( Z < 0.269 ) - P ( Z
< -0.115 ) =
0.6061 - 0.4541 =
0.1521 (answer)
3.4)
P ( X ≥ 16 ) = P( (X-µ)/σ ≥ (16-11.3) /
2.6)
= P(Z ≥ 1.808 ) = P( Z <
-1.808 ) = 0.0353
(answer)
answer: Yes
A normal population has mean = 9 and standard deviation -5. (a) What proportion of the...
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