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).

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this

a - base

b - exponent

so,