Answer:
The value is [tex]P( X < 155) = 0.18649 [/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = \$ 204[/tex]
The standard deviation is [tex]\sigma = \$ 55[/tex]
Generally the probability that another hotel will a rate lower than $155 per night is mathematically represented as
[tex]P( X < 155) = P( \frac{X - \mu }{\sigma} < \frac{155 - 204 }{ 55} )[/tex]
[tex]\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )[/tex]
=> [tex]P( X < 155) = P( Z < -0.8909 )[/tex]
From the z-table the area under the normal curve corresponding to -0.8909, towards the left is
[tex]P( Z < -0.8909 ) =0.18649[/tex]
=> [tex]P( X < 155) = 0.18649 [/tex]
