Respuesta :
Answer: 0.3061.
Step-by-step explanation:
Given : The temperature reading from a thermocouple placed in a constant-temperature medium is normally distributed with mean [tex]\mu[/tex], the actual temperature of the medium, and standard deviation [tex]\sigma[/tex].
Let X be the random variable that represents the reading of the thermometer.
Confidence level : [tex]=95\%[/tex]
We know that the z-value for 95% confidence interval is 1.96.
Then, we have
[tex]-1.96<\dfrac{X-\mu}{\sigma}<1.96[/tex] [tex]z=\dfrac{X-\mu}{\sigma}[/tex]
[tex]\Rightarrow\ -1.96\sigma<X-\mu<1.96\sigma[/tex]
But all readings are within 0.6° of [tex]\mu[/tex].
So, [tex]1.96\sigma=0.6[/tex]
[tex]\Rightarrow\ \sigma=\dfrac{0.6}{1.96}=0.30612244898\approx0.3061[/tex]
Hence, the required standard deviation will be
The confidence level is 95% in normal distribution then The value of standard deviation is 0.3061.
What is a normal distribution?
It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.
Given
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.
Let x be the random variable that represents the reading of the thermometer.
The confidence level is 95%. Then the z-value for 95% confidence level interval is 1.96.
Then we have
[tex]-\ \ 1.96 \ < \dfrac{x- \mu}{\sigma} < 1.96\\-1.96 \sigma < x- \mu \ < 1.96 \sigma[/tex]
But all the readings are within 0.6° of μ. Then
[tex]1.96 \sigma = 0.6\\[/tex]
On solving
[tex]\sigma = \dfrac{0.6}{1.96}\\\\\sigma = 0.306122 \approx 3061[/tex]
Thus, the standard deviation is 0.3061.
More about the normal distribution link is given below.
https://brainly.com/question/12421652
