Question

fill in the missing information. clyde clement wants to analyze a shipment of bags of cement. he knows the weight of the bags is normally distributed so he can use the standard normal distribution. he measures the weight of 600 randomly selected bags in the shipment. next, he calculates the mean and standard deviation of their weights. the mean is 50 lbs. and the standard deviation is 1.5 lbs. clyde uses the normal distribution table to calculate the number of bags in each segment of the distribution.

standard deviation	percentage from table	number of bags out of 600
-2 to -1 ( to 48.5 lbs )	%	82
-1 to 0 (48.5 to lbs )	34.1%
0 to +1 (50 to 51.5 lbs )	%
+1 to +2 (51.5 to lbs )	13.6%

Explanation:

Step1: Recall normal - distribution properties

In a normal distribution, if the mean $\mu = 50$ lbs and the standard deviation $\sigma=1.5$ lbs. For the first row, when $z=- 1$, $x=\mu+\sigma z=50 + 1.5\times(-1)=48.5$ lbs, when $z = - 2$, $x=\mu+\sigma z=50+1.5\times(-2)=47$ lbs. The percentage of data in the $z$-score range of $-2$ to $-1$ is $13.6\%$.

Step2: Calculate number of bags for $-1$ to $0$

If the percentage of data in the $z$-score range of $-1$ to $0$ is $34.1\%$, and the total number of bags $n = 600$, then the number of bags is $0.341\times600 = 204.6\approx205$.

Step3: Recall percentage for $0$ to $+1$

The percentage of data in the $z$-score range of $0$ to $+1$ in a normal - distribution is $34.1\%$.

Step4: Calculate number of bags for $0$ to $+1$

The number of bags in the $z$-score range of $0$ to $+1$ is $0.341\times600=204.6\approx205$.

Step5: Calculate upper - bound for $+1$ to $+2$

When $z = + 2$, $x=\mu+\sigma z=50 + 1.5\times2=53$ lbs.

Step6: Calculate number of bags for $+1$ to $+2$

The number of bags in the $z$-score range of $+1$ to $+2$ is $0.136\times600 = 81.6\approx82$.

Answer:

Standard Deviation	Percentage from table	Number of bags out of 600
-1 to 0 (48.5 to 50 lbs)	34.1%	205
0 to +1 (50 to 51.5 lbs)	34.1%	205
+1 to +2 (51.5 to 53 lbs)	13.6%	82