Answer:
The value is [tex]P(8 < X < 10 ) = 0.8186[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 10 .0[/tex]
The standard deviation is [tex]\sigma = 1[/tex]
Generally the probability that a single reading is between 8 and 10 is mathematically represented as
[tex]P(8 < X < 10 ) = P( \frac{8 - 10 }{ 1} < \frac{X - \mu }{ \sigma } < \frac{10 - 10 }{1} )[/tex]
[tex]\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )[/tex]
=> [tex]P(8 < X < 10 ) = P( -2 < Z< 1 )[/tex]
=> [tex]P(8 < X < 10 ) = P( Z< 1 ) - P( Z < -2 )[/tex]
From the z table the area under the normal curve to the left corresponding to 1 and -2 is
[tex]P( Z< 1 ) = 0.84134[/tex]
and
[tex]P( Z < -2 ) = 0.02275[/tex]
=> [tex]P(8 < X < 10 ) = 0.84134 - 0.02275[/tex]
=> [tex]P(8 < X < 10 ) = 0.8186[/tex]
