Question

Assume that the readings on scietific thermometers are normally distributed with a mean of 0 0C and a standard deviation of 1 0C . A thermometer is randomly selected and tested. Find the probability of the reading greater than -1.05 in degrees Celsius. (up to four decimal place, please)

Answer 1

Answer:  0.8531

Step-by-step explanation:

Let x be the random variable that represents the readings on scientific thermometers .

Given : The readings on scientific thermometers are normally distributed,

Population mean : $\mu=0^{\circ}\ C$

Standard deviation : $\sigma=1^{\circ}\ C$

Z-score : $z=\dfrac{x-\mu}{\sigma}$

Now, the z-value corresponding to -1.05 :  $z=\dfrac{-1.05.-0}{1}=-1.05$

P-value = $P(x>-1.05)=P(z>-1.05)=1-P(z\leq-1.05)$

$=1-0.1468591=0.8531409\approx0.8531\text{ (Rounded to four decimal places)}$

Hence, the probability of the reading greater than -1.05 in degrees Celsius.= 0.8531