The quality-control inspector of a production plant will reject a batch of syringes if two or more defective syringes are found in a random sample of ten syringes taken from the batch. Suppose the batch contains 1% defective syringes.   (a) Make a histogram showing the probabilities of  r = 0, 1, 2, 3,   ,  9 and 10 defective syringes in a random sample of ten syringes. A histogram has a horizontal axis labeled r with values from 0 to 10 and a vertical axis labeled P(r) with values from 0 to 1. The histogram has 11 bars. Each bar is associated with a label and an approximate value as listed below. 0: 0.31 1: 0.39 2: 0.21 3: 0.07 4: 0.02 5: 0 6: 0 7: 0 8: 0 9: 0 10: 0   A histogram has a horizontal axis labeled r with values from 0 to 10 and a vertical axis labeled P(r) with values from 0 to 1. The histogram has 11 bars. Each bar is associated with a label and an approximate value as listed below. 0: 0.18 1: 0.33 2: 0.29 3: 0.15 4: 0.05 5: 0.01 6: 0 7: 0 8: 0 9: 0 10: 0   A histogram has a horizontal axis labeled r with values from 0 to 10 and a vertical axis labeled P(r) with values from 0 to 1. The histogram has 11 bars. Each bar is associated with a label and an approximate value as listed below. 0: 0.9 1: 0.09 2: 0 3: 0 4: 0 5: 0 6: 0 7: 0 8: 0 9: 0 10: 0   A histogram has a horizontal axis labeled r with values from 0 to 10 and a vertical axis labeled P(r) with values from 0 to 1. The histogram has 11 bars. Each bar is associated with a label and an approximate value as listed below. 0: 0.54 1: 0.34 2: 0.1 3: 0.02 4: 0 5: 0 6: 0 7: 0 8: 0 9: 0 10: 0 (b) Find ?. (Enter your answer to two decimal places.) ? =  syringes What is the expected number of defective syringes the inspector will find? (Enter your answer to two decimal places.)  syringes (c) What is the probability that the batch will be accepted? (Round your answer to three decimal places.)   (d) Find ?. (Round your answer to three decimal places.) ? =  syringes

Let a be a random variable representing the percentage of protein content for early bloom alfalfa hay. The average percentage protein content of such early bloom alfalfa should be u = 17.2%. A farmer's co-op is thinking of buying a large amount of baled hay but suspects that the hay is from a later summer cutting with lower protein content. A small amount of hay was removed from each bale of a random sample of 50 bales. The average protein content from the samples was determined by a local agricultural college to be -15.8% with a sample standard deviation of S = 5.3%- At a = .05, does this hay have lower average protein content than the early bloom alfalfa?

In the airline business, "on-time" flight arrival is important for connecting flights and general customer satisfaction. Is there a difference between summer and winter average on-time flight arrivals? Let x1 be a random variable that represents percentage of on-time arrivals at major airports in the summer. Let x2 be a random variable that represents percentage of on-time arrivals at major airports in the winter. A random sample of n1 = 16 major airports showed that x1 = 74.9%, with s1 = 5.3%. A random sample of n2 = 18 major airports showed that x2 = 70.2%, with s2 = 8.6%. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value a small amount and thereby produce a slightly more "conservative" answer. (a) Does this information indicate a difference (either way) in the population mean percentage of on-time arrivals for summer compared to winter? Use α = 0.05. (i) What is the…

In a genetics experiment on​ peas, one sample of offspring contained 433 green peas and 121 yellow peas. Based on those​ results, estimate the probability of getting an offspring pea that is green. Is the result reasonably close to the value of 3/4 that was​ expected?