A manufacturer knows that their items have a normally distributed lifespan, with a mean of 13.9 years, and standard deviation of 2.9 years. If you randomly purchase 9 items, what is the probability that their mean life will be longer than 14 years

0.4588

Step-by-step explanation:

When we have random sample, the z score formula we use is:

z = (x-μ)/σ/√n

where x is the raw score = 14

μ is the population mean = 13.9

σ is the population standard deviation = 2.9

n is random number of samples = 9

z = 14 - 13.9/2.9/√9

z = 0.1/2.9/3

z = 0.10345

Probability value from Z-Table:

P(x<14) = 0.5412

P(x>14) = 1 - P(x<14) = 0.4588

The probability that their mean life will be longer than 14 years is 0.4588

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

step-by-step explanation:

we can use this expression to calculate the energy gain as a particle moves with a field or the energy loss as it moves against it. (note that it is also used to define the electron-volt, a unit of energy equal to that gained by an electron as it falls through a pd of 1 v, i.e. w = 1 ev = 1.6 10-19 c 1 v = 1.6 10-19j).in fact this expression is really nothing more than the statement that potential is the potential energy per unit charge. in this case, v= w/qis simply stating that the change in potential energy(or work done) per unit charge is equal to the change in potential (or potential difference), v.student questions: uniform electric fields2electron beamcathode+5 kvanode0 v