"Alexa wants to determine if the actual proportion of orders that are delivered late to the customers is different from the value reported by the initial data analysis. In a recent random sample of 200 orders, Alexa found that 12 orders are delivered late. To use a normal distribution in this scenario, which of the following conditions must be satisfied?"
a. Both n x Po and n x (1 - po) must be at least 10 where po is the null value for the population proportion.
b. Any two samples must be independent of each other.
c. There must be at least 10 observed successes and 10 observed failures in the sample.
d. The observations within the sample must be independent of each other.

Simplify the expression. enter the correct answer.

1. what is the formula for finding the vertical distance between two points on a coordinate plane?

Amachine that produces a special type of transistor (a component of computers) has a 2% defective rate. the production is considered a random process where each transistor is independent of the others. (a) what is the probability that the 10th transistor produced is the first with a defect? (b) what is the probability that the machine produces no defective transistors in a batch of 100? (c) on average, how many transistors would you expect to be produced before the first with a defect? what is the standard deviation? (d) another machine that also produces transistors has a 5% defective rate where each transistor is produced independent of the others. on average how many transistors would you expect to be produced with this machine before the first with a defect? what is the standard deviation? (e) based on your answers to parts (c) and (d), how does increasing the probability of an event a↵ect the mean and standard deviation of the wait time until success?