Business: 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

Johnson electronics makes calculators. consumer satisfaction

djub

04.01.2022

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$

=0.0495 (from standard table of Z )

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