Consider a manufacturing process called as turning (a type of machining process) that is used to manufacture cylindrical metal samples with a nominal diameter of 10.00 mm. past data from the manufacturer shows a variation in the diameter of samples that is given by a normal distribution with a standard deviation of 0.50 mm. if the specified tolerance on the diameter is 0.75 mm, roughly what percentage of samples manufactured using this process satisfy the tolerance specification?

86.64%

Step-by-step explanation:

Let x be a random variable that represents the diameter of metal samples.

Given : Population mean :

Standard deviation:

Specified tolerance on the diameter is 0.75 mm.

i.e. range of diameter = 10-0.75< x <10+0.75 = 9.25< x< 10.75

Formula to find the z-score corresponds to x:

At x= 0.75,  

Using standard normal table for z-value,

P-value :

∴ Percentage of samples manufactured using this process satisfy the tolerance specification = 86.64%

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752

a.)the line for function b is steeper