Question

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ruckload of 5000 electric drills. Exercise 7.2: The warehouse for a hardware store chain has just received a t Before accepting the shipment, the purchasing manager in for testing. He intend if the mean consumption for the sample is greater than 300 watts as listed on the product sists that a sample of the drills be randomly selected s to measure the maximum power consumption of each drill. He will reject the shipment ipment is the manufacturer's records of product tests showing the drills on the truck label. require an average of 295 watts with a standard deviation of 16 watts. Assume normal distiri consumption for population of drills. a. Find the probability that the truckload of drills will be rejected if he samples 25 drills b. Find the probability that the truckload of drills will be rejected if he samples 49 drills c. What are the impacts of larger sample size n on the mean and standard deviation among sample averages of power consumption (As and σ) and ts absolute values of z-score lzl ? Exercise 7.3: The life span of Good Old Everglo Bulbs follows a normal distribution with a mean life of 400 hours and a standard deviation of 30 hours. Assume infinite population of Good Old Everglo Bulbs. What is the probability that 4 bulbs selected at random will have an average life span of more than 445 hours?

Answer 1

Solution : ( 7.3 )

$\mathrm{Z=\frac{\overline{X}-\mu }{\frac{\sigma }{\sqrt{n}}}}=\frac{445-400}{\frac{30}{\sqrt{4}}}=\frac{45}{\frac{30}{\sqrt{4}}}=\frac{45\sqrt{4}}{30}=\frac{3\sqrt{4}}{2}=\frac{3*2}{2}=3$

$\mathrm{P(\overline{X}>445)=P(Z>3.0)=1-P(Z<3.0)}=1-0.99865=0.00135$

$\mathrm{Hence,\:the\:probability\:that\:4\:bulbs\:selected\:at\:random\:will\:have\:an\:average\:life\:span\:of\:more\:than\:445\:hours\:is\:\:\:\bold{0.00135}}$