Question

heres a link to the formula packet. this is a test review assignment. the purpose of this assignment is to help you prepare for the test. on the test, you wont have access to the videos or helps in the problems. you should try to do these problems without using these videos and additional helps. if you dont know what to do, you can watch the video. if the only way you can do the problems is watching the videos then you are not ready to take the test and should continue studying (you can request new problems and keep working on them after you get credit for the problems without impacting your grade). assume that the readings at freezing on a bundle of thermometers are normally distributed with a mean of 0°c and a standard deviation of 1.00°c. a single thermometer is randomly selected and tested. find the probability of obtaining a reading greater than 1.394°c. $p(z > 1.394)=$

Explanation:

Step1: Recall the properties of the standard normal distribution

The total area under the standard - normal curve is 1, and the standard normal distribution is symmetric about \(z = 0\). We know that \(P(Z>z)=1 - P(Z\leq z)\).

Step2: Use the standard - normal table

We look up the value of \(P(Z\leq1.394)\) in the standard - normal table (z - table). The standard - normal table gives the cumulative probability \(P(Z\leq z)\) for a given \(z\) value. Looking up \(z = 1.394\) (usually we can use \(z = 1.39\) since most z - tables have values to two decimal places), from the z - table, \(P(Z\leq1.39)=0.9177\).

Step3: Calculate \(P(Z > 1.394)\)

Using the formula \(P(Z>z)=1 - P(Z\leq z)\), we substitute \(z = 1.394\) (using the value from the table for \(z = 1.39\)). So \(P(Z>1.394)=1 - 0.9177 = 0.0823\).

Answer:

\(0.0823\)