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]
=> Â Â [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 Â
  [tex]P( Z <  -0.8909 ) =0.18649[/tex]
=> Â Â [tex]P( X < Â 155) Â = 0.18649 Â [/tex]
