Question

# a. Assume that x has a normal distribution with the specified mean and standard deviation. Find...

a. 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.)

? = 4.8; ? = 1.5

P(3 ? x ? 6) =

b. 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.)

? = 41; ? = 15

P(50 ? x ? 70) =

c. 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.)

? = 21; ? = 3.6

P(x ? 30) =

For given and , we convert this to standard normal as

P( X < x) = P( Z < x - / )

a)

For = 4.8, = 1.5

P( 3 <= X <= 6) = P( X <= 6) - P( X <= 3)

= P( Z <= 6 - 4.8 / 1.5) - P( X <= 3 - 4.8 / 1.5)

= P( Z <= 0.8) - P( Z < -1.2)

= P( Z < 0.8) - ( 1 - P( Z < 1.2) )

= 0.7882 - ( 1 - 0.8849)

= 0.6731

b)

For = 41, = 15

So,

P( 50 <= X <= 70) = P( X <= 70) - P( X <= 50)

= P( Z <= 70 - 41 / 15) - P( Z <= 50 - 41 / 15)

= P( Z <= 1.9333) - P( Z < 0.6)

= 0.9734 - 0.7257

= 0.2477

c)

For = 21 , = 3.6

So,

P( X >= 30) = P( Z >= 30 - 21 / 3.6)

= P( Z >= 2.5)

= 1 - P( Z < 2.5)

= 1 - 0.9938

= 0.0062

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