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

Answer:

the probability that exactly 30 of the 500 calculators IS 0.0495

Explanation:

Given data:

number of calculators n = 500,

percentage of defected calculators p = 0.05

From Normal approximation method;

$X~Normal mean = 500\times 0.05 = 25,$

$s = \sqrt{n\times p\times (1-p)}$

   $= \sqrt{(500\times 0.05\times 0.95)} = 4.87$

Therefore probability is

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

$=P[\frac{(29.5-25)}{4.87}] < \frac{(X-mean)}{s} < \frac{(30.5-25)}{4.87}

=P(0.92<Z< 1.13)$

=0.0495 (from standard table of Z )