Solution :
Given that ,
mean =
= 521
standard deviation =
= 110
a) P(x < 400 ) = P[(x -
) /
< (400 - 521) /110 ]
= P(z < -1.1 )
= 0.1357
proportion = 0.1357
b)
P( 400< x < 550 ) = P[( 400 - 521 )/110 ) < (x -
) /
<
(550-521 ) /110 ) ]
= P(-1.1 < z < 0.26 )
= P(z <0.26 ) - P(z < -1.1)
Using standard normal table
= 0.6026 - 0.1357 = 0.4669
proportion = 0.4669
c)
P(x >550 ) = 1 - p( x< 550)
=1- p [(x -
) /
< (550-521) /110 ]
=1- P(z < 0.26 )
= 1 - 0.6026 = 0.3974
proportion = 0.3974
d)
P(Z < z ) = 0.10
z = -1.282
Using z-score formula,
x = z *
+
x = -1.282 * 110+521
x = 380
e)
P(Z > z ) = 0.10
1- P(z < z) =0.10
P(z < z) = 1-0.10 = 0.90
z = 1.282
Using z-score formula,
x = z *
+
x = 1.282 *110+521
x = 662
Bringing all of section 6.2 together... The scores on the SAT verbal test in recent years...
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The scores on the SAT verbal test in recent years follow approximately the normal distribution distribution. Students get a mean score of 517 with a standard deviation of 111. Use technology to answer these questions. a. What is the proportion of students scoring under 400 (4 decimal positions)? b. What is the proportion of students scoring between 400 and 5507 (4 decimal positions) c. What is the proportion of students scoring over 5507 (4 decimal positions) d. How high must...
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