Answer to Question #229873 in Statistics and Probability for Soa

Question

A racing car is one of the many toys manufactured by Mack Corporation. The assembly times for this 

toy follow a normal distribution with a mean of 110 minutes and a standard deviation of 5 minutes. The 

company closes at 8 PM every day and Mr. Y starts to assemble a racing car at 6 PM. 

(i) What is the probability that he will finish this job before the company closes for the day?

(ii) Show the required area graphically indicating both X and Z scaling.

Answer 1

Given the following information:

$\overline{x}=110\:minutes$

$\sigma =5\:minutes$

(i). The closing time is: 8 P.M

Starting time of Mr. Y to assemble is: 6 P.M

$For\:x=120$

$z=\frac{120-110}{5}=-2\:$

$P\left(x\le 120\right)=P\left(z\le 2\right)=.0228$ (The z value for -2 is obtained from the z - table)

Thus, the probability is .0228 that this worker will finish assembling this racing car before the company closes for the day.

(ii).

The shaded area in the required area in the figure above indicating graphically both X and Z scaling.