Mathematics, 23.01.2020 05:31 Bloom247

(a) find z such that the proportion of observations that are less than z in a standard normal distribution is 0.36. (enter your answer rounded to two decimal places.)

(b) find z such that 36% of all observations from a standard normal distribution are greater than z. (enter your answer rounded to two decimal places.)

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Answer from: rr3908661

a) z = -0.358

b) z = 0.358

Step-by-step explanation:

We are given a standard normal distribution.

a) We have to find the value of z such that the proportion of observations that are less than z in a standard normal distribution is 0.36.

That is,

P(Z

This value will be calculated with the help of a standard normal table.

From standard normal table we have,

$P(z\leq -0.358) = 0.36$

Thus, for z equal to -0.358 the proportion of observations that are less than z in a standard normal distribution is 0.36

b) We have to find the value of z such that 36% of all observations from a standard normal distribution are greater than z.

P(Zz) = 0.36

This value will be calculated with the help of a standard normal table.

= 1 -P( Z z)=1 - 0.36 = 0.64

$P( z \leq z)=0.64$

Calculation the value from standard normal z table, we have,

$P(z \leq 0.358) = 0.64$

Thus, 36% of all observations from a standard normal distribution are greater than z equal to 0.358

Answer from: Quest

the central idea is that:

individuals should refuse to cooperate with institutions they believe unjust.

thoreau felt that governments were more often agents of corruption than justice, even democracies, and that just because the majority feels a certain way does not make it just or correct in absolute terms. he uses the fact that slavery exists in our democracy to support this idea.

he goes on to say that, as a result, people should live true to their own internal laws regarding right and wrong, as a product of reflection and a moral life, rather than following every law that society imposes.

step-by-step explanation:

Answer from: Quest

$a_1 = 1$ , and

$a_{n+1} = a_n + (n + 1)$ for $n \ge 1$

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote $a_1 = 1$ , $a_2 = 3$ , $a_3 = 6$ , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from $a_1 = 1$ , to get to $a_2 = 3$ , we add $2(=1+1)$

from $a_2 = 3$ , to get to $a_3 = 6$ , we add $3 (=2+1)$

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

$a_1 = 1$ , and $a_{n+1} = a_n +(n + 1)$ for $n \ge 1$

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