Question

Temperature transducers of a certain type are shipped in batches of 50. A sample of 60 batches was selected, and the number of transducers in each batch not conforming to design specifications was determined, resulting in the following data:

2 1 2 4 0 1 3 2 0 5 3 3 1 3 2 4 7 0 2 3 0 4 2 1 3 1 1 3 4 1
2 3 2 2 8 4 5 1 3 1 5 0 2 3 2 1 0 6 4 2 1 6 0 3 3 3 6 1 2 3

Required:
a. Determine frequencies and relative frequencies for the observed values of x = number of nonconforming transducers in a batch.
b. What proportion of batches in the sample have at most six nonconforming transducers?
c. What proportion have fewer than six? (Enter your answer to three decimal places.)
d. What proportion have at least six nonconforming units?

Answer 1

Kindly check explanation

Explanation:

X ___ Frequency ___ relative Frequency %

0_____7 ________11.67

1_____12________20.00

2____ 13 ________21.67

3____ 14 ________23.33

4 ____6 ________10.00

5____ 3 _________5.00

6 ____3 _________5.00

7_____1 _________1.67

8 ____ 1 _________1.67

B.)

(x = 0) + (x = 1) + (x = 2) + (x = 3) + (x = 4) + (x = 5) + (x = 6)

(11.67 + 20.00 + 21.67 + 23.33 + 10.00 + 5.00 + 5.00) = 96.67% = 0.967 (3 decimal places)

C.)

(x = 0) + (x = 1) + (x = 2) + (x = 3) + (x = 4) + (x = 5)

(11.67 + 20.00 + 21.67 + 23.33 + 10.00 + 5.00) = 91.67% = 0.917 (3 decimal places)

D.)

(x = 6) + (x = 7) + (x = 8)

(5.00 + 1.67 + 1.67)% = 8.34% = 0.0834