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To be considered as a menu item for Gloria's new restaurant an item must have scored in the top 15% by the food critics in the area. The average item's score is 7 with a standard deviation of 2. Assuming that the variable is normally distributed, find the lowest score possible for a menu item to still be considered?

Respuesta :

Answer:

Lowest score needed=4.92

Step-by-step explanation:

Using the standard normal distribution table we find the value of standard normal deviate corresponding to area of 15%

For area of 15% we have Z= -1.04

Thus we have

[tex]Z=\frac{X-\overline{X}}{\sigma }\\\\\therefore X=\sigma Z+\overline{X}\\\\[/tex]

Applying values we get

[tex]X=-1.04\times 2+7\\\\X=4.92[/tex]

Thus lowest score needed = 4.92

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