Show that if X is a discrete random variable a mean of mu and a standard deviation sigma, then Z=(X-mu)/sigma is a discrete random variable with a mean of zero and a standard deviation of 1
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Q: Assume that adults have IQ scores that are normally distributed with a mean of μ=105 and a standard…
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Q: Assume that adults have IQ scores that are normally distributed with a mean of μ=100 and a standard…
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Q: Assume that adults have IQ scores that are normally distributed with a mean of μ=105 and a standard…
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Q: Assume that adults have IQ scores that are normally distributed with a mean of mu equals 105 and a…
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Q: Assume that adults have IQ scores that are normally distributed with a mean of μ=100 and a standard…
A: given datanormal distributionμ=100σ=20x = IQ score,p(x<124) = ?
Q: Assume that adults have IQ scores that are normally distributed with a mean of μ=100 and a standard…
A: Given : Assume that adults have IQ scores that are normally distributed with a mean of μ=100 and a…
Q: Assume that adults have IQ scores that are normally distributed with a mean of μ=100 and a standard…
A: Assume that adults have IQ scores that are normally distributed with a mean of μ=100 and a standard…
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Q: Assume that adults have IQ scores that are normally distributed with mean of mu = 100 and a standard…
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Q: Assume that adults have IQ scores that are normally distributed with a mean of mμ=100 and a standard…
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Q: Assume that adults have IQ scores that are normally distributed with a mean of μ=105 and a standard…
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Show that if X is a discrete random variable a
Z=(X-mu)/sigma is a discrete random variable with a mean of zero and a standard deviation of 1
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In SD(X-mu/sigma)=1/sigma * SD(X)
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- The probability that a randomly chosen student in a statistics class submits his/her homework on time is 0.12. There is 35 student in the class. Each student does his/her homework independently. What is the standard deviation of X, where X is the number of students who submit the homework on time?Assume that adults have IQ scores that are normally distributed with a mean of µ = 100 and a standard deviation o = 20. Find the probability that a randomly selected adult has an IQ between 80 and 120.The time required to roast a duck may be taken to have a normal distribution with a mean of 45 minutes and standard deviation 12 minutes. The time required to roast a chicken may be taken to have an independent normal distribution with mean 30 minutes and standard deviation 8 minutes. Assume that the oven can only roast one poultry at one time. 0.338 One duck is chosen at random. Find the probability that at least 50 minutes will be required to roast it. (ii) Three randomly chosen ducks are roasted successively in random order. Find the probability that each of them requires more than 45 minutes to roast. 0.15
- 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 = !Weights of Lamb after eight weeks after born are normally distributed with mean µ = 14 kg and variance σ 2 = 4. a)Find the probability p that a single lamb has weight less than 12 kg. b) Find the probability that exactly 3 of the next 5 lambs examined will have weights less than 12 kg.fast
- Customers arrive on average every 30 minutes to The Grease Monkey, an auto repair shop with only one mechanic. The inter-arrival times are exponentially distributed. Repair times are variable with a mean of 25 minutes and a standard deviation of 20 minutes. The mechanic works on one vehicle at a time from beginning to end and takes in any waiting vehicles on a first-come first-served basis. The garage itself has room for only one vehicle at a time, so waiting vehicles are kept in the parking lot where there are always plenty of spaces available. Assume customers never balk or renege. a)What is the average number of cars in the garage (not including the parking lot)? b) How long (in minutes) do vehicles wait on average in the adjacent parking lot? c) The competitor shop across the street also has a single mechanic and an average of 3.1 vehicles waiting in its parking lot. The competitor only does oil changes, which take an average of 21 minutes. Customer inter-arrival times to the…The level of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) in the exhaust over the useful life (150,000 miles of driving) of cars of a particular model varies Normally with mean 90 mg/mi and standard deviation of 4 mg/mi. A company has 25 cars of this model in its fleet. Find the level L such that the probability that the average NOX + NMOG level bar x for the fleet greater than L is only 0.03? Round final answer to three decimals.Assume that adults have IQ scores that are normally distributed with a mean of μ=105 and a standard deviation σ=15. Find the probability that a randomly selected adult has an IQ less than 123.
- Let x be a continuous random variable that is normally distributed with a mean of 123.5 and a standard deviation of 12.3. FInd the probability that x assumes a value between 97.9 and 113.2.Service time for a customer coming through a checkout counter in a retail store is a random variable with the mean of 1.0 minutes and standard deviation of 0.5 minutes. Suppose that the distribution of service time is fairly close to a normal distribution. Suppose there are two counters in a store, n = 11 customers in the first line and n2 = 30 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 0.5 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 = iAssume that adults have IQ scores that are normally distributed with a mean of μ=105 and a standard deviation σ=15. Find the probability that a randomly selected adult has an IQ between 89 and 121.