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Bringing all of section 6.2 together... The scores on the SAT verbal test in recent years follow approximately the N(521, 110

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Answer #1

Solution :

Given that ,

mean = \mu = 521

standard deviation = \sigma = 110

a) P(x < 400 ) = P[(x - \mu ) / \sigma < (400 - 521) /110 ]

= P(z < -1.1 )

= 0.1357

proportion = 0.1357

b)

P( 400< x < 550 ) = P[( 400 - 521 )/110 ) < (x - \mu ) /\sigma  < (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 - \mu ) / \sigma < (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 * \sigma + \mu

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 * \sigma + \mu

x = 1.282 *110+521

x = 662

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