## (a) A shipment of 120 fasteners that contains 4 defective fasteners was sent to a manufacturing plant. The quality-control manager at the ma

(a) A shipment of 120 fasteners that contains 4 defective fasteners was sent to a manufacturing plant. The quality-control manager at the manufacturing plant randomly selects 5 fasters and inspects them. What is the probability that exactly 1 fastener is defective? (b) The Energy Information Administration (EIA) sampled 900 retail gasoline outlets and reported that, the national average gasoline price for regular-grade gasoline to be $4.113 per gallon with a standard deviation of $0.11 per gallon. Construct a 95% Confidence Interval for mean price of regular-grade gasoline price.

## Answers ( )

Answer:a) Probability that exactly 1 fastener is defective, P(X = 1) = 0.144

b) Confidence interval for mean price,

Step-by-step explanation:a) Total number of fasteners = 120

Number of defective fasteners = 4

Probability of selecting a defective fastener, p = 4/120

p = 0.033

Probability of selecting an undefective fastener, q = 1 – p

q = 1 – 0.033

q = 0.967

5 fasteners were randomly selected, n =5

Probability that exactly one fastener is defective:

b) Number of gasoline outlets sampled, n = 900

Average gasoline price,

Standard deviation,

Confidence Level, CL = 95% = 0.95

Significance level,

From the standard normal table,

error margin can be calculated as follows:

The confidence interval will be given as: