Question

Please answer the questions below

1. Use the standard normal table to find the​ z-score that corresponds to the cumulative area 0.7071. If the area is not in the​ table, use the entry closest to the area. If the area is halfway between two​ entries, use the​ z-score halfway between the corresponding​ z-scores.

2. Use the standard normal table to find the​ z-score that corresponds to the cumulative area 0.9629. If the area is not in the​ table, use the entry closest to the area. If the area is halfway between two​ entries, use the​ z-score halfway between the corresponding​ z-scores.

3. The weights of bags of baby carrots are normally​ distributed, with a mean of 32 ounces and a standard deviation of 0.34 ounce. Bags in the upper​ 4.5% are too heavy and must be repackaged. What is the most a bag of baby carrots can weigh and not need to be​ repackaged?

Answer 1

Solution:

Question 1) Find z value such that:

P( Z < z) = 0.7071

Look in z  table for Area = 0.7071 or its closest area and find corresponding z value.

From above table we can see area 0.7071 is in between 0.7054 and 0.7088 and both are at same distance from 0.7071, Hence corresponding z values are 0.54 and 0.55

Thus average of both z values is = ( 0.54+0.55) / 2 = 0.545

Thus z = 0.545

Question 2)

Find z value such that:

P( Z < z) = 0.9629

Look in z  table for Area = 0.9629 or its closest area and find corresponding z value.

From above table we can see area 0.9629 is in between 0.9625 and 0.9633 and both are at same distance from 0.9629 , Hence corresponding z values are 1.78 and 1.79

Thus average of both z values is = ( 1.78+1.79) / 2 = 1.785

Thus z = 1.785

Question 3)

Given:  The weights of bags of baby carrots are normally ​distributed, with a mean of 32 ounces and a standard deviation of 0.34 ounces.

Bags in the upper​ 4.5% are too heavy and must be repackaged. Then remaining 100-4.5=95.5% need not to be​ repackaged.

What is the most a bag of baby carrots can weigh and not need to be​ repackaged?

that is find x value such that:

P( X< x) = 95.5%

P( X < x) = 0.9550

Look in z  table for Area = 0.9550 or its closest area and find corresponding z value.

Area 0.9554  is closest to 0.9550 and it corresponds to 1.7 and 0.00

that is  z = 1.70

Now use following formula to find x value:

ounce.

the most a bag of baby carrots can weigh 32.578 ounce  and not need to be​ repackaged.