Normal Distribution

Question 11 pts

Let X be a standard normal random variable. Find P(X < 0). Express your answer as a decimal.

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Let X be a standard normal random variable. Find P(X
$\le$ -2.27). Express your answer as a decimal.

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Let X be a standard normal random variable. Find P(X > 2.82). Express your answer as a decimal.

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Let X be a standard normal random variable. Find P(-1.20 < X < 1.74). Express your answer as a decimal.

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Assume that thermometer readings are normally distributed with a mean of 0 degrees Celsius and a standard deviation of 1 degree Celsius. A thermometer is randomly selected and tested. Find the temperature reading that separates the bottom 93.7% from the top 6.3%. Round your answer to the nearest hundredth.

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Assume that thermometer readings are normally distributed with a mean of 0 degrees Celsius and a standard deviation of 1 degree Celsius. A thermometer is randomly selected and tested. Find the temperature reading that separates the bottom 40.9% from the top 59.1%. Round your answer to the nearest hundredth.

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A radar unit is used to measure speeds of cars on a motorway. The speeds are normally distributed with a mean of 90 km/hr and a standard deviation of 10 km/hr. What is the probability that a car picked at random is travelling at more than 100 km/hr?

Round your answer to the nearest thousandth.

Flag this QuestionQuestion 81 pts

A survey by the National Retail Federation found that women spend on average $146.21 for the Christmas holidays. Assume the standard deviation is $29.44. Find the percentage of women who spend less than $160.00. Assume the variable is normally distributed. Express the answer in the form of a percentage (do not include % sign in your answer). Round your answer to the nearest hundredth.

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Each month, an American household generates an average of 28 pounds of newspaper for garbage or recycling. Assume the standard deviation is 2 pounds. If a household is selected at random, find the probability of its generation between 27 and 31 pounds per month. Assume the variable is normally distributed. Express your answer as a percentage. (do not include % sign in your answer). Round your answer to the nearest hundredth.

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The national average SAT score (for Verbal and Math) is 1028. If we assume a normal distribution with standard deviation 92, what is the probability that a randomly selected score exceeds 1200? Express your answer as a decimal. Round your answer to the nearest hundredth.

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To qualify for a police academy, candidates must score in the top 10% on a general abilities test. The test has a mean of 200 and a standard deviation of 20. Find the lowest possible score to qualify. Assume the test scores are normally distributed.

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The average price of a personal computer is $949. If the computer prices are normally distributed with a standard deviation of $100, the least expensive 10% of personal computers cost less than what amount? Round your answer to the nearest dollar.