The mean of a normal distribution is 400 pounds. The standard deviation is 10 pounds. What is the probability of a weight between 415 pounds and the mean of 400 pounds

The probability is

Step-by-step explanation:

From the question we are told that

   The population mean is  

   The  standard deviation is  

   The considered values are  

Given that the weight follows a normal distribution

     i.e      

Now the probability of a weight between 415 pounds and the mean of 400 pounds is mathematically as

So   is equal to Z (the standardized value of  X  )

Hence we have  

substituting values

From the standardized normal distribution table   and

So

NOTE :  This above  values obtained from the standardized normal distribution table can also be obtained using the P(Z) calculator at  (calculator dot net).

what is the question? i am guessing you are looking for the area.

to find an area, you have to do length x width.

in this case, it would be 12 ft x 4 ft = 48 sq. ft

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm