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assume that the random variable X is normally distributed, with mean ? = 50 and standard deviation ? = 7. Compute the following probabilities. Be sure to draw a normal curve with the area corresponding to the probability shaded.

P(56 < X < 68)

B- find the value of za.

z 0.02

C-assume that the random variable X is normally distributed, with mean ? = 50 and standard deviation ? = 7. Find each indicated percentile for X.

The 90th percentile

D-the graph of a normal curve is given. Use the graph to identify the values of ? and ?.

Respuesta :

Answer:

Step-by-step explanation:

Given that  the random variable X is normally distributed, with

mean  = 50 and standard deviation  = 7.

Then we have z= [tex]\frac{x-50}{7} is N(0,1)[/tex]

Using this and normal table we find that

a) [tex]P(56<x<68)\\= P(0.86<Z<2.57)\\=0.4949-0.3051\\=0.1898[/tex]

b) When z=0.02

we get

[tex]x=50+0.02(7)=50.14[/tex]

c) 90th percentile z value =1.645

90th percentile of X [tex]=50+7(1.645)\\= 50+11.515\\=61.515[/tex]

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