An engineer designed a valve that will regulate water pressure on an automobile engine. the engineer designed the valve such that it would produce a mean pressure of 7.6 pounds/square inch. it is believed that the valve performs above the specifications. the valve was tested on 140 engines and the mean pressure was 7.8 pounds/square inch. assume the standard deviation is known to be 1.0. a level of significance of 0.05 will be used. make a decision to reject or fail to reject the null hypothesis.

The valves perform above expectations.

Step-by-step explanation:

We are given the following information in the question:

Population mean, μ = 7.6 pounds per square inch

Sample size, n = 140

Sample mean, = 7.8 pounds per square inch

Population standard deviation = 1.0 pounds per square inch

Level of significance = 0.05

We design the null and alternate hypothesis:

:  μ = 7.6 pounds per square inch

:  μ > 7.6 pounds per square inch

Formula:

Now, we are performing a one tail test with level of significance of 0.05, we calculate the critical value of z with the help of standard normal distribution table.

Thus, = 1.645

Result:

Since,

is rejected.

Thus, we accept the alternate hypothesis.

Hence, the valve perform above expectations.

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.

7 is the median   7.875 is the mean

step-by-step explanation:

3,4,5,6,8,11,13,13