What is the probability that the investment has a return of 10% or less? (2 marks). A person must score in the upper 5% of the population on an IQ test to qualify for a particular occupation. If IQ scores are normally distributed with a mean of 100 and a standard deviation of 15, what score must a person have to qualify for this occupation? (4 marks

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The weights of a certain breed of dogs follow a normal distribution with a mean of 30 pounds and a standard deviation of 5 pounds. If a random sample of 25 dogs is selected, what is the probability that their average weight is between 28 and 32 pounds? The monthly returns on a stock follow a normal distribution with a mean return of 2% and a standard deviation of 4%. What is the probability that the stock has a negative return in any given month? The lifetimes of a certain brand of lightbulb are normally distributed with a mean of 1000 hours and a standard deviation of 100 hours. What is the probability that a randomly selected lightbulb will last more than 1100 hours?

Service time for a customer coming through a checkout counter in a retail store is a random variable with the mean of 4.0 minutes and standard deviation of 2.0 minutes. Suppose that the distribution of service time is fairly close to a normal distribution. Suppose there are two counters in a store, n₁ = 46 customers in the first line and n₂ = 52 customers in the second line. Find the probability that the difference between the mean service time for the shorter line X₁ and the mean service time for the longer one X₂ is more than 0.3 minutes. Assume that the service times for each customer can be regarded as independent random variables. Round your answer to two decimal places (e.g. 98.76). P = !