In an advertisingcampaign, a snack company claimed that every18-ounce bag of its cookies contained at least 1000 chocolate chips. Two statisticians attempted to verify the claim. The accompanying data represent the number of chips in an18-ounce bag of thecompany's cookies based on their study. Complete parts(a) through(e).

Click here to view the chocolate chip data table.LOADING...

Click here to view the standard normal distribution table (page 1).LOADING...

Click here to view the standard normal distribution table (page 2).LOADING...

(a) Draw a normal probability plot to determine if the data could have come from a normal distribution.

Choose the correct plot below.

A.

1000

1300

1600

-2.5

0

2.5

Observedvalue

Expectedz-score

A coordinate system has a horizontal axis labeled Observed value from 1000 to 1600 in increments of 50 and a vertical axis labeled Expected z-score from negative 2.5 to 2.5 in increments of 0.5. There are 40 plotted points, each of which is above all plotted points to its left. From left to right, the points follow the general pattern of a smooth curve that rises at a slightly decreasing rate and then rises at a slightly increasing rate. From left to right, the plotted points include the following: (1090, negative 1.24); (1095, negative 1); (1130, negative 0.68); (1165, negative 0.4); (1210, negative 0.2); (1225, negative 0.02); (1270, 0.16); (1295, 0.36); (1365, 0.62); (1445, 1); (1510, 1.24). All coordinates are approximate.

B.

1000

1300

1600

-2.5

0

2.5

Observedvalue

Expectedz-score

A coordinate system has a horizontal axis labeled Observed value from 1000 to 1600 in increments of 50 and a vertical axis labeled Expected z-score from negative 2.5 to 2.5 in increments of 0.5. There are 40 plotted points, each of which is above all plotted points to its left. From left to right, the points roughly follow the pattern of a curve that rises at a slightly decreasing rate and then rises at a slightly increasing rate. From left to right, the plotted points include the following: (1090, negative 2.22); (1095, negative 1.58); (1130, negative 1.4); (1165, negative 0.74); (1210, negative 0.62); (1225, negative 0.52); (1270, 0.1); (1295, 0.22); (1365, 0.86); (1445, 1.08); (1510, 1.72). All coordinates are approximate.

C.

1000

1300

1600

-2.5

0

2.5

Observedvalue

Expectedz-score

A coordinate system has a horizontal axis labeled Observed value from 1000 to 1600 in increments of 50 and a vertical axis labeled Expected z-score from negative 2.5 to 2.5 in increments of 0.5. There are 40 plotted points, each of which is above all plotted points to its left. The points follow a pattern of straight line that rises from left to right. From left to right, the plotted points include the following: (1090, negative 1.54); (1095, negative 1.52); (1130, negative 1.14); (1165, negative 0.8); (1210, negative 0.38); (1225, negative 0.22); (1270, 0.22); (1295, 0.5); (1365, 1.16); (1445, 1.96); (1510, 2.62). All coordinates are approximate.

D.

1000

1300

1600

-2.5

0

2.5

Observedvalue

Expectedz-score

A coordinate system has a horizontal axis labeled Observed value from 1000 to 1600 in increments of 50 and a vertical axis labeled Expected z-score from negative 2.5 to 2.5 in increments of 0.5. There are 40 plotted points, each of which is above all plotted points to its left. From left to right, the points follow the general pattern of a smooth curve that rises at a slightly decreasing rate and then rises at a slightly increasing rate. From left to right, the plotted points include the following: (1090, negative 2.16); (1095, negative 1.74); (1130, negative 1.2); (1165, negative 0.7); (1210, negative 0.34); (1225, negative 0.04); (1270, 0.28); (1295, 0.64); (1365, 1.08); (1445, 1.74); (1510, 2.16). All coordinates are approximate.

(b) Determine the mean and standard deviation of the sample data.

The mean of the sample data is

.

(Round to one decimal place asneeded.)

The standard deviation of the sample data is

.

(Round to one decimal place asneeded.)

(c) Using the sample mean and sample standard deviation obtained in part(b) as estimates for the population mean and population standarddeviation, respectively, draw a graph of a normal model for the distribution of chips in a bag of cookies.

A.

Observed value

900

1200

1500

1800

A graph titled Observed Value has a horizontal axis labeled from 900 to 1800 in increments of 50. A symmetric curve with a single peak at its center falls at an increasing and then decreasing rate on both sides, approaching the axis from above. A vertical line segment runs from the curve's peak to the axis at approximate coordinate 1150, labeled mu. The curve has inflection points at approximate coordinates 1070 and 1220.

B.

Observed value

600

1000

1400

1800

A graph titled Observed Value has a horizontal axis labeled from 600 to 1800 in increments of 50. A symmetric curve with a single peak at its center falls at an increasing and then decreasing rate on both sides, approaching the axis from above. A vertical line segment runs from the curve's peak to the axis at approximate coordinate 1100, labeled mu. The curve has inflection points at approximate coordinates 970 and 1220.

C.

Observed value

1000

1400

1800

2200

A graph titled Observed Value has a horizontal axis labeled from 1000 to 2200 in increments of 50. A symmetric curve with a single peak at its center falls at an increasing and then decreasing rate on both sides, approaching the axis from above. A vertical line segment runs from the curve's peak to the axis at approximate coordinate 1450, labeled mu. The curve has inflection points at approximate coordinates 1320 and 1570.

D.

Observed value

900

1200

1500

1800

A graph titled Observed Value has a horizontal axis labeled from 900 to 1800 in increments of 50. A symmetric curve with a single peak at its center falls at an increasing and then decreasing rate on both sides, approaching the axis from above. A vertical line segment runs from the curve's peak to the axis at approximate coordinate 1250, labeled mu. The curve has inflection points at approximate coordinates 1150 and 1350.

(d) Using the normal model from part(c), find the probability that an18-ounce bag of chips selected at random contains at least 1000 chips.

The probability is

.

(Round to three decimal places asneeded.)

(e) Using the normal model from part(c), find the probability that an18-ounce bag of chips selected at random contains between 1200 and 1500 chips.

The probability is

.

(Round to three decimal places asneeded.)

Click to select your answer(s).