Question

Number 1

riple of U.s you that the l hours Ch. 11 Test Review A normal distribution has mean u and distribution. Find the following probabi For 4-6, a normal distribution has a mea selected x-value from the distribution i

Answer 1

P(< x < $\mu + \sigma$ )

P(mu - 2 sigma lessthanorequalto x lessthanorequalto mu + sigma) = P((mu - 2 sigma - mu)/sigma lessthanorequalto (X - mu)/sigma lessthanorequalto (mu + sigma - mu)/sigma) = P( - 2 lessthanorequalto Z lessthanorequalto 1) = P(Z lessthanorequalto 1) - P(Z lessthanorequalto - 2) = 0.8413 - 0.0228 = 0.8185

= P(( $\mu - 2\sigma - \mu$ )/ $\sigma$ < (X - $\mu$ )/ $\sigma$ < ( $\mu + \sigma - \mu$ )/ $\sigma$ )

= P(-2 < Z < 1)

= P(Z < 1) - P(Z < -2)

= 0.8413 - 0.0228

= 0.8185