1) Assume that x has a normal distribution with the specified mean and standard
ID: 3048707 • Letter: 1
Question
1)
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.)
= 4.9; = 2.0
P(3 x 6) =
2)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.)
= 15.7; = 3.8
P(10 x 26) =
3)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.)
= 42; = 14
P(50 x 70) =
4)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.)
= 5.5; = 1.4
P(7 x 9) =
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.)
= 14.0; = 2.8
P(8 x 12) =
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.)
= 49; = 14
P(40 x 47) =
7)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.)
= 23; = 4.1
P(x 30) =
8)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.)
= 106; = 12
P(x 120) =
9)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.)
= 109; = 12
10)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.)
= 2.5; = 0.39
P(x 2)
11)Find z such that 9.3% of the standard normal curve lies to the left of z. (Round your answer to two decimal places.)
z =
Sketch the area described.
P(x 90) =
Explanation / Answer
1)
Since =4.9 and =2.0 we have:
P ( 3<X<6 )=P ( 34.9< X<64.9 )=P ( (34.9)/2.0<(X)/<(64.9)/2.0)
Since Z=x/ , (34.9)/2.0=0.95 and (64.9)/2.0=0.55 we have:
P ( 3<X<6 )=P ( 0.95<Z<0.55 )
Use the standard normal table to conclude that:
P ( 0.95<Z<0.55 )=0.5377
2) Since =15.7 and =3.8 we have:
P ( 10<X<26 )=P( 1015.7< X<2615.7 )=P((1015.7)/3.8<(X)/<(2615.7)/3.8)
Since Z=(x)/ , (1015.7)/3.8=1.5 and (2615.7)/3.8=2.71 we have:
P ( 10<X<26 )=P ( 1.5<Z<2.71 )
Use the standard normal table to conclude that:
P ( 1.5<Z<2.71 )=0.9298
3) Since =42 and =14 we have:
P ( 50<X<70 )=P (5042< X<7042 )=P ((5042)/14<(X)/<(7042)/14)
Since Z=(x)/ , (5042)/14=0.57 and (7042)/14=2 we have:
P ( 50<X<70 )=P ( 0.57<Z<2 )
Use the standard normal table to conclude that:
P ( 0.57<Z<2 )=0.2615
4) Since =5.5 and =1.4 we have:
P ( 7<X<9 )=P (75.5< X<95.5 )=P ((75.5)/1.4<(X)/<(95.5)/1.4)
Since Z=(x)/ , (75.5)/1.4=1.07 and (95.5)/1.4=2.5 we have:
P ( 7<X<9 )=P ( 1.07<Z<2.5 )
Use the standard normal table to conclude that:
P ( 1.07<Z<2.5 )=0.1361
5) Since =14 and =2.8 we have:
P ( 8<X<12 )=P (814< X<1214 )=P ((814)/2.8<(X)/<(1214)/2.8)
Since Z=(x)/ , (814)/2.8=2.14 and (1214)/2.8=0.71 we have:
P ( 8<X<12 )=P ( 2.14<Z<0.71 )
Use the standard normal table to conclude that:
P ( 2.14<Z<0.71 )=0.2227
6) Since =49 and =14 we have:
P ( 40<X<47 )=P (4049< X<4749 )=P ((4049)/14<(X)/<(4749)/14)
Since Z=(x)/ , (4049)/14=0.64 and (4749)/14=0.14 we have:
P ( 40<X<47 )=P ( 0.64<Z<0.14 )
Use the standard normal table to conclude that:
P ( 0.64<Z<0.14 )=0.1832
7) Since =23 and =4.1 we have:
P ( X>30 )=P ( X>3023 )=P ((X)/>(3023)/4.1)
Since Z=(x)/ and (3023)/4.1=1.71 we have:
P ( X>30 )=P ( Z>1.71 )
Use the standard normal table to conclude that:
P (Z>1.71)=0.0436
I HAVE DONE THE FIRST SEVEN QUESTIONS. . PLEASE REPOST REST QUESTIONS. THANK YOU.
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