Assume that x has a normal distribution, with the specified mean and standard deviation.?

Assume that x has a normal distribution, with the specified mean and standard deviation. I need to find the indicated probabilities;


a)P(40%26lt;X%26lt;47); mean=50; standard deviation=15


b)P(X%26gt;2); mean=3; standard deviation=0.25


c)Find z such that 97.5% of the standard normal curve lies to the left of z


d)Find z such that 95% of the standard normal curve lies to the right of z

Assume that x has a normal distribution, with the specified mean and standard deviation.?
For any normal random variable X with mean μ and standard deviation σ, X ~ Normal(μ, σ)





you can translate into standard normal units by:


Z = (X - μ) / σ





where Z ~ Normal(μ = 0, σ = 1). You can then use the standard normal cdf tables to get probabilities.





a)





X ~ Normal(μ = 50, σ = 15)





P( 40 %26lt; X %26lt; 47 )


= P( (40 - 50) / 15 %26lt; Z %26lt; (47 - 50) / 15)


= P( - 2/3 %26lt; Z %26lt; - 1/5)


= P( Z %26lt; - 1/5) - P( Z %26lt; - 2.3)


= 0.4207403 - 0.2524925


= 0.1682478





---------





b)





X ~ Normal(μ = 3, σ = 0.25)





P( X %26gt; 2)


= P(Z %26gt; (2 -3 ) / 0.25)


= P( Z %26gt; -4)


= 0.9999683





----------





c)





P( Z %26lt; z ) = 0.975





z = 1.96





------------------





d)





P(Z %26gt; z) = 0.95





z = -1.645
Reply:You need a table for that..look at the back of your book..

snapdragon2