Need help with how they arrived with 3.43

[V51773]

Hello

ive been trying to understand the formula and utilization of z table, but i seem to be stuck on how this solution arrived with using 3.43 with the given.

I tried flipping the formula to various ways like 1-7/ 0.04 even went as far as multiplying that or reversing the Z formula but i cant seem to land to anywhere near 3.43.

 

[Dr.Peterson]

Hello

ive been trying to understand the formula and utilization of z table, but i seem to be stuck on how this solution arrived with using 3.43 with the given.

I tried flipping the formula to various ways like 1-7/ 0.04 even went as far as multiplying that or reversing the Z formula but i cant seem to land to anywhere near 3.43.

Please show the problem you are trying to solve. And are you saying this is the supplied "correct" solution, or your own work?

 

[V51773]

Hi im trying to learn(diy) it myself

the question was


A manufacturer of calculators finds that the operating lifetime is normally distributed with a
mean life of seven years. The manufacturer finds that under a one-year warranty, 4% of the
calculators are returned. If 10 000 calculators are manufactured, find the expected number that
will last longer than nine years.

The above was the supplied solution, im trying to understand how he reversed computing for z to arrive at 3.43

 

[BigBeachBanana]

Hello

ive been trying to understand the formula and utilization of z table, but i seem to be stuck on how this solution arrived with using 3.43 with the given.

I tried flipping the formula to various ways like 1-7/ 0.04 even went as far as multiplying that or reversing the Z formula but i cant seem to land to anywhere near 3.43.

[math] F\left(\frac{1-7}{\sigma}\right)=0.04\\ \frac{1-7}{\sigma}=F^{-1}(0.04)\\ [/math]What's the z-value corresponding to 0.04?
Note that due to symmetry of the normal distribution, [imath]F^{-1}(0.04)=-F^{-1}(0.96)[/imath]

 

[V51773]

.5160 chief

 

[BigBeachBanana]

.5160 chief

That's incorrect. I can't tell what and how you're looking up the z-table. Perhaps post a snipet.

 

[V51773]

Ohhh if its 0.4 then .96 then then z is 1.7?

Is this correct?

 

[BigBeachBanana]

Ohhh if its 0.4 then .96 then then z is 1.7?

Is this correct?

Close. Do you see 0.9599 corresponds to 1.75? So [imath]F^{-1}(0.96)=1.75 \implies F^{-1}(0.04)=-1.75[/imath]. Thus, [imath]\frac{1-7}{\sigma}=-1.75[/imath]
You can take it from here.