Probability Question

Question

The barton Company manufactures automobile charge indicator gauges. Under test conditions, these gauges are supposed to read 0 volts. However, some gauges read slightly more than 0 volts and some slightly less. Let z=voltage reading of a gauge under test conditions so each gauge has a value of z. Past experience has shown that z is approximately normal with a mean of 0 and a standard deviation of 1. If a gauge is selected at random what is the probability that its voltage reading with be anywhere between 0 and 1.43 volts?

Answer 1

Hi John.

 

This is a normal distribution problem and we need to use a normal table.  When determining the probability of a result between two numbers, as between 0 and 1.43, we need to calculate Z for each of those points, look them up in the table and take the difference.

 

In this case mean = 0 and standard deviation = 1 so Z = the given z.

 

Recall the formula for Z is 

 

Z = (x-μ)/σ

 

In this case x = z

 

Z = (0-0)/1 = 0

and

Z = (1.43-0)/1 = 1.43

 

Using a Z table

 

Z₀  = .5000

 

Z_1.43 = .9236

 

Probability (0<z<1.43) = .9236 - .5 = .4236 = 42.36%

 

Note the z tables I use are the ones that give the probability of z < a given number.  I believe this to be the most common.  However, there are tables that give the probability of z > a given number or probability .5<z<a given number.