A chocolate factory produces mints that weigh 10 grams apiece. The standard deviation of the weight of a box of 10 mints is 3 grams. You buy a box of mints that weighs 95 grams. What is your confidence that the box you bought did not come from the factory?

90%
95%
10%
5%

The confidence that the box you bought did not come from the factory is 90 %.

Step-by-step explanation:

Since we have given that

Population Mean weight (\mu)= 10 grams a piece

Standard deviation of the weight of a box = 3 grams

Number of mints = 10

We need to buy a box of mints that weighs 95 grams.

Sample mean is given by

x = grams .

First we find out the standard error which is given by

= 0.94868

Since it is normal distribution, so, we will find z-score.

z = - 0.53

The area to the left of a z-score of -0.53 = 0.29805.

So, it may be 90% or 95 % confidence.

For 95% confidence level,

Similarly,

For 90% confidence level,

The value is much smaller than 0.05.  

So, we will get 90% confidence and the critical value = 1.645

Margin of error is given by

(Standard deviation) (critical\ value) = 0.94868 1.645

                                                              =1.56

So, confidence interval will be

                          (10-1.56,10+1.56)

                              =(8.44,11.56)

the quotient is 4x^2 - 27x + 167 with a remainder of -996

step-by-step explanation:

in synthetic division, use -6 as the divisor and use the coefficients {4, -3, 5, 6}:

-6     )   4     -3     5     6

                -24   162 -1002

          4   -27   167   -996

thus, the quotient is 4x^2 - 27x + 167 with a remainder of -996.

note:   your "4x°-3x+5x+6" is ambiguous / incomplete.   i had to assume that you meant '4x^3 - 3x^2 + 5x + 6."

d

step-by-step explanation:

given

y + 3 = - 4(x - 2) ← distribute the parenthesis

y + 3 = - 4x + 8 ( subtract 3 from both sides )

y = - 4x + 5 → d