1. A small sample of toys has 50 spinning tops in a toy manufacturing company. 2% of the spinning tops are defective. We randomly select 4 of these toys out of this sample. What is the discrete probability distribution of the defective toys in the sample?

2.Surface-finish defects in a small electric appliance occur at random with a mean rate of 0.2 defects per unit. Find the probability that a randomly selected unit will contain at least three surface-finish defect.

3.The output voltage of a power supply is normally distributed with mean 110 V and standard deviation 0.08 V. If the lower and upper specifications for voltage are 109.95 V and 110.05 V, respectively, what is the probability that a power supply selected at random will conform to the specifications on voltage?

4. A battery manufacturer tests its batteries based on an acceptance plan. It randomly selects 50 batteries, and does the acceptance test. If at least 48 batteries pass the test, the entire product would be accepted. There are 2500 batteries and 2% of the batteries are defected. What is the probability of the product to be accepted?

5. The tensile strength of a fiber used in manufacturing cloth is of interest to the purchaser. Previous experience indicates that the standard deviation of tensile strength is 5 psi. A random sample of 15 fiber specimens is selected, and the average tensile strength is found to be 180 psi. Construct a 95% lower confidence interval on the mean tensile strength.