Question

The cross section of a plastic tube for use in pulmonary resuscitators is normally
distributed with a mean of 12.5mm2 and a standard deviation of 0.2 mm2. When the
cross section is less than 12mm2 or more than 13 mm2, the tube will not be adjusted
properly. What is the probability that a randomly selected tube will be adjusted
properly?

A. 0.9538 B. 0.9998 C. 0.9890 D. 0.9745 E. 0.9876

Answer 1

Solution :

Given that ,

mean = $\mu$ = 12.5

standard deviation = $\sigma$ = 0.2

P(12 < x < 13) = P[(12 - 12.5)/ 0.2) < (x - $\mu$) /$\sigma$  < (13 - 12.5) / 0.2) ]

= P(-2.50 < z < 2.50)

= P(z < 2.50) - P(z < -2.50)

Using z table,

= 0.9938 - 0.0062

= 0.9876

correct option is = E