The temperature reading from a thermocouple placed in a constant-temperature medium is normally distributed with mean μ, the actual temperature of the medium, and standard deviation σ. what would the value of σ have to be to ensure that 95% of all readings are within 0.1° of μ? (round your answer to four decimal places.)

The standard deviation would have to be 0.05.

Step-by-step explanation:

We can solve this problem using the 68-95-99.7 rule for normal distributions:

The rule states that:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviations of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

What would the value of σ have to be to ensure that 95% of all readings are within 0.1° of μ?

This means that 2 standard deviations would need to be within 0.1 of the mean. So

The standard deviation would have to be 0.05.

34

step-by-step explanation:

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3