Answer:
the probability of less than 15.97 will be (16-7)/16 =0.5625
Step-by-step explanation:
To ascertain the manager claim, we use the normal distribution curve.
z= (x − x')/ σ
, where
z is called the normal standard variate,
x is  the value of the variable, =15.97
x' is the mean value of  the distribution =16
σ is the standard deviation  of the distribution= 0.24
so, z= (15.97 - 16)/ 0.24 = -0.125
Using  a table of normal distribution to check the partial areas beneath the standardized  normal curve,  a z-value of −0.125  corresponds to an area of 0.0498 between the mean  value.The negative  z-value shows that it lies to the left of the z=0  ordinate.
The total area under the standardized normal curve  is unity and since the curve is symmetrical, it follows  that the total area to the left of the z=0 ordinate is  0.5000. Thus the area to the left of the z=−0.125 ordinate is 0.5000−0.0498 = 0.4503 of the  total area of the curve.
therefore, the probability of the average weight equal to 15.97 ounces is 0.4503.
For a group of 16 packages, 16×0.4503 = 7.2, i.e. 7 packages will have the weight of 15.97 ounces.
the probability of less than 15.97 will be (16-7)/16 =0.5625
