Mathematics Assignment - Desklib

Mathematics Assignment
Student Name:
Instructor Name:
Course Number:
10th July 2019
1a)

z= x−μ
σ
When x=1.72, μ=1.5 , σ =0.1
z= 1.72−1.5
0.1 =2.2
P(X>1.72)=P(Z>2.2)=1-(0.4861+0.5)=0.0139
P(X>1.72) =0.0139
b)
z= x−μ
σ
When x=1.35, μ=1.5 , σ =0.1
z= 1.35−1.5
0 .1 =−1.5
P(Z<-1.5)=0.5-0.4332=0.0668
P(X<1.35)= P(Z<-1.5)=0.0668
c)
z= x−μ
σ
When x=1.45, μ=1.5 , σ =0.1
z= 1.45−1.5
0.1 =−0.5
P(Z=-0.5)=1-0.6915=0.3185
When x=1.62, μ=1.5 , σ =0.1
z= 1.62−1.5
0.1 =1.2
P(Z=1.2)=0.8849
P(1.45 ≤X≤ 1.62¿=¿P(-0.5≤Z≤1.2)=0.8849-0.3185=0.5664
P(1.45≤X≤ 1.62¿=¿P(-0.5≤Z≤1.2)=0.1915+0.3849=0.5764
2.
P(defective)=0.15
P(0 or 1 defective)= P(0 defective)+ P(1 defective)
10C0(0.15)0(0.85)10 +10C1(0.15)1(0.85)9

=0.1969+0.3474=0.5443
P(accepting shipment)=0.5443
3.a)
mean= 400+3800
2 =¿2100
mean =$2100
b)
standard deviation= b−a
√12 = 3800−400
√12 = 3400
√12 =981.5
standard deviation=$ 981.5
c)
3800-400=3400
b-a=2000-400=1600
P(less than $2000)= 1600
3400 =0.4706
P(less than 2000)¿ 0.4706
d)
3800-3000=800
P(more than $3000)= 800
3400 =0.2353
P(more than $3000)¿ 0.2353
e)
P(exactly $2500)¿ 1−¿ P(more than $2500)+ P(less than $ 2500) ¿
P(exactly $2500)¿ 1−¿ 3800−2500
3400 + 2500−400
3400
P(exactly $2500)¿ 1− ( 1300
3400 + 2100
3400 )=0
4. )

a) z= x−μ
σ
When x=300, μ=250 , σ =2500
z= 300−250
2500 =0.02
P(x>300)=P(Z>0.02)=0.5-0.008=0.492
b)
When x=190, μ=250 , σ =2500
z= 190−250
2500 =−0.024
When x=270, μ=250 , σ =2500
z= 270−250
2500 =0.008
P(190<x<270)=P(-0.024 ¿Z<0.008)=(0.008+0.004)=0.012
c)
When x=260, μ=250 , σ =2500
z= 260−250
2500 =0.004
P(x≤260)=P(Z≤0.02)=
d) 90
100 ×250 hours=225 hours
e) 0.05×250 hours=12.5 hours
5. a)i
P(between 15 and 20 defective items)= P(15 defective ) or P(16 defective)or P(17
defective)or P(18
defective)or P(19 defective)or P(20 defective)
P(between 15 and 20 defective items)= 100C15(0.10)15(0.90)85 +100C16(0.10)16(0.90)84+
+100C17(0.10)17(0.90)83+100C18(0.10)18(0.90)82+100C19(0.10)19(0.90)81+100C20(0.10)20(0.90
)80