Answer: a) 0.9544996
b) 0.9999366
Step-by-step explanation:
Given : The actual measured resistances of wires produced by company A have a normal probability distribution with mean ohm and standard deviation
ohm.
Wires manufactured for use in a computer system are specified to have resistances between .12 and .14 ohms.
Let x be the random variable that represents the value of resistance in wires.
Using formula for z-score ,
The z-value at x= 0.12 will be
The z-value at x= 0.14 will be
The p-value :
Hence, the probability that a randomly selected wire from company A’s production will meet the specifications = 0.9544996
b) Sample size : n= 4
Using formula for z-score ,
The z-value at x= 0.12 will be
The z-value at x= 0.14 will be
The p-value :
The probability that all four in a randomly selected system will meet the specifications = 0.9999366