Parts (a) and (b) are both related to normal distribution but are not directly connected to each other. Please complete both parts. 2. Sketch two normal pdfs, both withu=-1, but one with (a) o =2 and the other with o = 7. Label the curves. (b) Compute P(|Z|< 2.43). Assume that Z is a standard normal random variable

Suppose X is a non-standard normal variable, with a mean of 139, and std deviation of 15 (i.e. X~N(139,15)). You have an observation (z) on a standard normal scale (i.e. Z~N(0,1)). If z =  1.29, what is it on an X scale?  How can I calculate this using excel & by hand?

Suppose X is a random variable of a normal distribution with E(X)=2 and Var(X)=4. Find P(X<4)

Please do a, e, and f only

Standing eye heights of women normally distributed with a mean of 1516 mm and a standard deviation of 63 mm.  What % of women have a standing eye height between 1420 mm and 1560 mm, and what is the probability that a group of 20 women has an average standing eye height that is less than 1500 mm? Even though the sample size is less than 30, why can the Central Limit Theorem still be applied?

a) Find  such that P( X < ? ) = 0.9332, where X is a normal random variable with mean = 10 and standard deviation  = 2.5.  b) Find  such that P( X > ?) = 0.1230, where X is a normal random variable with mean    = 10 and standard deviation  = 2.5.

Suppose X is a non-standard normal variable, with a mean of 118, and std deviation of 15 (i.e. X~N(118,15)). You have an observation (z) on a standard normal scale (i.e. Z~N(0,1)). If z =  -0.03, what is it on an X scale?

Assume that the random variable X is normally distributed with mean = 15 and standard deviation = 2. Let n = 4.  Find P( > 16) and P( < 16).

i need help with c

You are hired by the governor to study whether a tax on liquor has decreased average liquor consump- tion in your state. You are able to obtain, for a sample of individuals selected at random, the difference in liquor consumption (in ounces) for the years before and after the tax. For person i who is sampled randomly from the population, Y, denotes the change in liquor consumption. Treat these as a random sample from a Normal(µ, o²) distribution. (i) The null hypothesis is that there was no change in average liquor consumption. State this formally in terms of µ. (ii) The alternative is that there was a decline in liquor consumption; state the alternative in terms of µ. (iii) Now, suppose your sample size is n = 900 and you obtain the estimates ỹ = -32.8 and s = 466.4. Calculate the t statistic for testing Ho against H¡; obtain the p-value for the test. (Because of the large sample size, just use the standard normal distribution tabulated in Table G.1.) Do you reject H, at the 5% level?…