Suppose X is a normally distributed random variable with mean 0 and variance 1 (i. e., standard normal). Compute the following (Hint: you can use the R functions pnorm and qnorm to answer these questions).
P r(X < 1:96)
P r(X > 1:64)
P r(0:5 < X < 0:5) 1% quantile, q:01 and 99% quantile, q:99 ? 5% quantile, q:05 and 95% quantile,

Step-by-step explanation:

Given

--- Mean

--- Variance

Calculate the standard deviation

Solving (a): P(X < 1.96)

First, we calculate the z score using:

This gives:

The probability is then solved using:

From the standard normal distribution table

So:

Solving (b): P(X > 1.64)

First, we calculate the z score using:

This gives:

The probability is then solved using:

From the standard normal distribution table

So:

Solving (c): P(0.5 < X < 0.5)

This can be split as:

In probability:

becomes

konichiwa~! my name is zalgo and i am here to answer your anime-related question today. more than likely, kirishima would kill izuku, marry mino and kiss momo. all of this would be my opinion by the way. (and i am also a weeb lol)

i hope this you! : d

stay and stay proud! " - zalgo

(and do you think you can mark me as brainliest? i'd greatly appreciate it! arigato~! )

describing distributions is one of the key skills you’ll need to earn a high score on the ap statistics exam. if you need proof of this, just flip through some past exam questions, which can be found at the collegeboard website. you’ll notice that the first free response question is almost always a question requiring you to look at a graph and describe it.

step-by-step explanation: just trying to get points sorry : (