When it is operating properly, a chemical plant has a daily production rate that is normally distributed with a mean of 885 tons/day and a standard deviation of 42 tons/day. During an analysis of period, the output is measured with random sampling on 60 consecutive days, and the mean output is found to be x=875 tons/day. The manager claims that at least 95 % probability that the plant is operating properly. Is he right? Justify your answer!

The test statistic Z = 1.844 < 1.96 at 0.05 level of significance

Null hypothesis is accepted

Yes he is right

The manager claims that at least 95 % probability that the plant is operating properly

Step-by-step explanation:

Explanation:-

Given data Population mean

                                           μ     = 885 tons /day

Given random sample size

                                          n = 60

mean of the sample

                                        x⁻  = 875 tons/day

The standard deviation of the Population

                                      σ = 42 tons/day

Null hypothesis:- H₀: The manager claims that at least 95 % probability that the plant is operating properly

Alternative Hypothesis :H₁: The manager do not claims that at least 95 % probability that the plant is operating properly

Level of significance =  0.05

The test statistic

|Z| = |-1.844| = 1.844

The tabulated value

The calculated value Z = 1.844 < 1.96 at 0.05 level of significance

Null hypothesis is accepted

Conclusion:-

The manager claims that at least 95 % probability that the plant is operating properly

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

arithmetic sequence

step-by-step explanation:

given that a sequence has terms as

19, 15, 11,

this is represented on a graph

the pattern indicates that the sequence is an arithmetic sequence with i term

a=19 and common difference d =-4

any general term

thus the sequence is reduced by 4 for each successive term starting from 1 and nth term is

24-5n.

first negative term would start after 5th term

5th term =24-25< 0

from 5th term onwards the sequence would be negative.