Question

A government entity sets a Food Defect Action Level (FDAL) for the various foreign substances that inevitably end up in the foods we eat. The FDAL level for insect filth in peanut butter is 0.60 insect fragment (larvae, eggs, body parts, and so on) per gram. Suppose that a supply of peanut butter contains 0.60 insect fragment per gram. Compute the probability that the number of insect fragments in a 7-gram sample of peanut butter is

(a) exactly five. (Round to four decimal places as needed.)

Fill in the blanks to complete the statement below.

About _____ (16,18, 13, 15) of every 100 7-gram samples of this supply will contain exactly 5 insect fragments.

(b) fewer than five. (Round to four decimal places as needed.)

Fill in the blanks to complete the statement below.

About _____ (59,61, 57, 58) of every 100 7-gram samples of this supply will contain fewer than 5 insect fragments.

(c) at least five. (Round to four decimal places as needed.)

Fill in the blanks to complete the statement below.

About _____ (38,41, 44, 42) of every 100 7-gram samples of this supply will contain at least 5 insect fragments.

(d) at least one. Interpret the results. (Round to four decimal places as needed.)

Fill in the blanks to complete the statement below.

About _____ (101,99, 96,100) of every 100 7-gram samples of this supply will contain at least 1 insect fragments.

(e) Would it be unusual for a 7-gram sample of this supply of peanut butter to contain seven or more insect fragments?

It would ______(be, not be) unusual. About ____ (11, 14, 16, 13) of every 100 7-gram samples of this supply will contain at least 7 insect fragments.

Answer 1

(a) exactly five. (Round to four decimal places as needed.)

Fill in the blanks to complete the statement below.

About 16 of every 100 7-gram samples of this supply will contain exactly 5 insect fragments.

(b) fewer than five. (Round to four decimal places as needed.)

Fill in the blanks to complete the statement below.

About 59 of every 100 7-gram samples of this supply will contain fewer than 5 insect fragments.

(c) at least five. (Round to four decimal places as needed.)

Fill in the blanks to complete the statement below.

About 41 of every 100 7-gram samples of this supply will contain at least 5 insect fragments.

(d) at least one. Interpret the results. (Round to four decimal places as needed.)

Fill in the blanks to complete the statement below.

About 99 of every 100 7-gram samples of this supply will contain at least 1 insect fragments.

(e) Would it be unusual for a 7-gram sample of this supply of peanut butter to contain seven or more insect fragments?

It would not be unusual. About 13 of every 100 7-gram samples of this supply will contain at least 7 insect fragments.

	4.2	mean rate of occurrence
		cumulative
X	P(X)	probability
0	0.0150	0.0150
1	0.0630	0.0780
2	0.1323	0.2102
3	0.1852	0.3954
4	0.1944	0.5898
5	0.1633	0.7531
6	0.1143	0.8675
7	0.0686	0.9361
8	0.0360	0.9721
9	0.0168	0.9889
10	0.0071	0.9959
11	0.0027	0.9986
12	0.0009	0.9996
13	0.0003	0.9999
14	0.0001	1.0000
15	0.0000	1.0000
16	0.0000	1.0000
17	0.0000	1.0000
18	0.0000	1.0000
19	0.0000	1.0000
20	0.0000	1.0000
	1.0000
	4.200	expected value
	4.200	variance
	2.049	standard deviation