Mathematical Methods · Unit 3 · Discrete random variables · Binomial distributions
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A survey of 200 households recorded the number of streaming service subscriptions per household. The data follows a normal distribution with mean 2.8 and standard deviation 1.2. Use this information to find the probability that a randomly selected household has no more than 4 subscriptions. Give your answer to three decimal places.
A manufacturer produces electronic components with a defect rate of $8\%$. A quality control team randomly selects 15 components from a batch and tests them. Use the language of probability to determine the probability that at most 2 components are defective.
A survey of 150 customers at a bookstore records the number of books purchased during a visit. The results are shown in the table below. What is the probability that a randomly selected customer purchased at least 3 books but fewer than 6 books?
A random sample of 200 residents in a regional town was surveyed about weekly spending on groceries. The sample mean was $\$145$ and the standard deviation was $\$32$. Use this information to estimate the number of residents in the sample who spent no more than $\$177$ per week on groceries.
A supermarket records the number of items purchased by customers in a single transaction. The results for 150 customers are shown in the table below. Which of the following statements correctly describes the probability that a randomly selected customer purchased at least 8 items but no more than 14 items?