Question

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) =

Answer #1

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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