Question

1, A police officer randomly selected 585 police records of larceny thefts. The accompanying data represent the number of offenses for various types of larceny thefts.

​(a)	Construct a probability model for type of larceny theft.
​(b)	Are coin-operated machine larcenies​ unusual?
​(c)	Are bicycle larcenies ​unusual?

​(a) Complete the table below.

Type of Larceny Theft	Number of Offenses
Pocket picking	9
Purse snatching	10
Shoplifting	124
From motor vehicles	222
Motor vehicle accessories	64
Bicycles	37
From buildings	108
From coin-operated machines	11

​(Round to three decimal places as​ needed.)

2, A baseball player hit 61 home runs in a season. Of the 61 home​ runs, 17 went to right​ field,20 went to right center field, 12 went to center​ field, 11 went to left center​ field, and 1 went to left field.

​(a)	What is the probability that a randomly selected home run was hit to right​ field?
​(b)	What is the probability that a randomly selected home run was hit to left​ field?
​(c)	Was it unusual for this player to hit a home run to left​ field? Explain.

​(Round to three decimal places as​ needed.)

Answer 1

(1)

(a)

A probability model for type of larceny theft is constructed as follows:

Type of Larceny Theft (x)	Probability (p)
Pocket picking	9/585 = 0.015
Purse snatching	10/585 = 0.017
Shoplifting	124/585 = 0.212
From motor vehicles	222/585 = 0.379
Motor vehicle accessories	64/585 = 0.109
Bicycles	37/585 = 0.063
From buildings	108/585 =0.185
From coin-operated machines	11/585 = 0.019

​(b)

Coin-operated machine larcenies​ are unusual because the probability of Coin-operated machine larcenies​ = 0.019 = 1.90% is less than 5%

(c)

Bicycle larcenies ​are not unusual because the probability of Bicycle larcenies ​= 0.063 = 6.30 % is greater than 5%.

(2)

(a)

the probability that a randomly selected home run was hit to right​ field = 17/61 = 0.279

(b)

the probability that a randomly selected home run was hit to left​ field = 1/61 = 0.016

(c)

it was unusual for this player to hit a home run to left​ field because the probability that a randomly selected home run was hit to left​ field = 1/61 = 0.016 = 1.60 % less than 5%