Question

a phlebotomist draws the blood of a random sample of 50 patients and determines their blood types as shown. complete parts (a) through (e). o o a o o b o b a o b b a b o o o a o a ab o a ab a a a o a a o a o b a o o ab o b ab o a a o a o a a o (a) construct a relative frequency distribution. (type integers or decimals. do not round.) blood type relative frequency a ab b o

Explanation:

Step1: Count frequencies of each blood type

First, we count the number of times each blood type appears in the data:

• Blood Type A: Let's count. Looking at the data:

Row 1: A
Row 2: A
Row 3: A
Row 4: A
Row 5: A, A, A
Row 6: A, A, A
Row 7: A, A, A
Row 8: A, A, A
Wait, let's do it carefully. Let's list all:

First column: O, B, B, O, AB, A, O, O, O, O
Second column: O, O, B, O, O, A, A, AB, A, O
Third column: A, B, A, O, A, A, O, A, O, A
Fourth column: O, A, B, A, AB, O, B, AB, A, A
Fifth column: O, O, B, O, A, A, A, O, A, O

Now count A:
First column: 1 (row 5)
Second column: 2 (rows 5,6)
Third column: 4 (rows 1,3,5,6,7,8? Wait, maybe better to count each cell:

Total cells: 10 rows ×5 columns =50 cells (since sample size is 50).

Let's count A:

Row 1: A (1)
Row 2: A (1)
Row 3: A (1)
Row 4: A (1)
Row 5: A, A, A (3)
Row 6: A, A, A (3)
Row 7: A, A, A (3)
Row 8: A, A, A (3)
Wait, no, let's count each occurrence:

Looking at the data:

First column (10 entries): O, B, B, O, AB, A, O, O, O, O → A:1
Second column (10 entries): O, O, B, O, O, A, A, AB, A, O → A:3 (rows 6,7,9)
Third column (10 entries): A, B, A, O, A, A, O, A, O, A → A:6 (rows 1,3,5,6,8,10)
Fourth column (10 entries): O, A, B, A, AB, O, B, AB, A, A → A:4 (rows 2,4,9,10)
Fifth column (10 entries): O, O, B, O, A, A, A, O, A, O → A:4 (rows 5,6,7,9)

Now sum A: 1 + 3 + 6 + 4 + 4 = 18

Blood Type AB:
First column: AB (1)
Second column: AB (1)
Fourth column: AB, AB (2)
Total: 1 + 1 + 2 = 4

Blood Type B:
First column: B, B (2)
Second column: B (1)
Third column: B (1)
Fourth column: B, B (2)
Fifth column: B (1)
Total: 2 + 1 + 1 + 2 + 1 = 7

Blood Type O:
Total sample size is 50. So O frequency = 50 - (A + AB + B) = 50 - (18 + 4 + 7) = 50 - 29 = 21. Let's verify:

First column: O, O, O, O, O (wait, first column: O (row1), B (2), B (3), O (4), AB (5), A (6), O (7), O (8), O (9), O (10) → O: 1,4,7,8,9,10 → 6
Second column: O (1), O (2), B (3), O (4), O (5), A (6), A (7), AB (8), A (9), O (10) → O:1,2,4,5,10 →5
Third column: A (1), B (2), A (3), O (4), A (5), A (6), O (7), A (8), O (9), A (10) → O:4,7,9 →3
Fourth column: O (1), A (2), B (3), A (4), AB (5), O (6), B (7), AB (8), A (9), A (10) → O:1,6 →2
Fifth column: O (1), O (2), B (3), O (4), A (5), A (6), A (7), O (8), A (9), O (10) → O:1,2,4,8,10 →5
Total O: 6 + 5 + 3 + 2 + 5 = 21. Correct.

Step2: Calculate relative frequencies

Relative frequency = (Frequency of blood type) / (Total number of patients) = Frequency / 50.

• For A: 18 / 50 = 0.36
• For AB: 4 / 50 = 0.08
• For B: 7 / 50 = 0.14
• For O: 21 / 50 = 0.42

Answer:

Blood Type	Relative Frequency
AB	0.08
B	0.14
O	0.42