Managerial statistics PDF

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Mandatory assignment for Business Management Year 3...

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BCM 411: MANAGERIAL STATISTICS – CAT 1. In a recent survey, 90% of the homes in a city were found to have colored TV’s. In a sample of nine homes, what is the probability that: Overall distribution to be applied. X has a binomial distribution with N=9 and p=0.9 Therefore, i. P ( X=9 )= ii.

P ( X=x ) =

9! N! 0.9x (0.1)N −x px (1−p) N− x = x ! ( 9−x ) ! x ! ( N −x ) !

All nine have colored TV’s? 9! 0.9 9 (0.1)0=0.99= 0.3874 9 ! ( 0) ! Less than five have colored TV’s?

P ( X 5 ) =1 −0.008331094 =0.9917 iv.

At least seven homes have colored TV’s?

The probability required is,

P ( X ≥ 7 )=P ( X=7 )+ P ( X =8) + P( X=9)

P ( X=7 )=

9! 0.97 (0.1 )2=0.1722 7! (2 ) !

P ( X=8 )=

9! 0.98 (0.1 )1=0.3874 8 ! (1 ) !

P ( X=8 )=

9! 0.9 9 (0.1)0 =0.3874 9 ! (0 ) !

P ( X ≥ 7 )=0.1722+0.3874+ 0.3874=0.947 2. A random sample of 50 auto drivers insured with a company and having similar auto insurance policies was selected. The following data shows monthly auto insurance premium (in Kshs.000) paid by them. 54

40

45

20

60

30

35

40

55

70

20

15

45

60

45

25

15

30

25

18

35

25

45

56

59

25

27

39

50

56

20

25

30

30

41

25

56

48

45

25

35

60

55

48

38

34

60

60

60

64

i) Group the above data starting with the class 10 -20 exclusive Class (KSHS. 000) 10-20

Tally

Frequency 3

20-30

11

30-40

9

40-50

11

50-60

8

60-70

7

70-80

1

ii) Represent the data using a Histogram and an Ogive and determine the mode and median (See scanned photos attached at the end of the word document) Class (KSHS. 000) 10-20

Frequency 3

Cumulative frequency...