Question

Johnson Electronics makes calculators. Consumer satisfaction is one of the top priorities of the company's management. The company guarantees the refund of money or a replacement for any calculator that malfunctions within two years from the data of purchase. It is known from past data that despite all efforts, 5% of the calculators manufactured by this company malfunction within a 2-year period. The company recently mailed 500 such calculators to its customers.Find the probability that exactly 30 of the 500 calculators will be returned for refund or replacement within a 2-year period.

Answer 1

the probability that exactly 30 of the 500 calculators IS 0.0495

Step-by-step explanation:

Given data:

number of calculators n = 500,

percentage of defected calculators p = 0.05

From Normal approximation method;

`X~Normal mean = 500* 0.05 = 25,`

`s = √(n* p* (1-p))`

`= √((500* 0.05* 0.95)) = 4.87`

Therefore probability is

P(X= 30) = P(29.5< X< 30.5) ( from continuous correction)

`=P[((29.5-25))/(4.87)] < ((X-mean))/(s) < ((30.5-25))/(4.87) </p><p> =P(0.92<Z< 1.13)`

=0.0495 (from standard table of Z )