If the random variable X is normally distributed with a mean equal to .45 and a standard deviation equal to .40, then P(X ≥ .75) is: (a) 0.2266 (b) 0.4525 (c) 0.7734 (d) 0.7500 (e) None of the above
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- Suppose X is a random variable of uniform distribution between 1 and 7. Find E(X)If XX represents a random variable coming from a normal distribution and P(X<10.2)=0.22P(X<10.2)=0.22, then P(X>10.2)=0.78P(X>10.2)=0.78. true or false5. The sediment density (g/cm³) from water in the Red River flowing through Winnipeg, Manitoba has a distribution with mean value 2.65 and standard deviation 0.85. If 40 random samples of water are collected, what is the approximate probability that the average sample sediment density is between 2.65 and 3.00? (Retain two decimal places in all calculations.) Mean value :2.45 40 samples. P (z.u5sx<3.w)?
- Let the random variable X denote the length of time (in seconds) required to complete a certain task. Suppose that the completion times are normally distributed with a mean of 216 seconds and a standard deviation of 50 seconds. (i) Find the probability that the time needed to complete the task is between 260 and 290 seconds. (ii) Find the value of k if P(X < k) = 0.025. (iii) A random sample of 25 similar tasks is selected. Find the probability that the mean completion time will be more than 200 seconds.Suppose a random sample of 25 students is selected from a community college where the scores on the final exam (out of 125 points) are normally distributed having mean equal to 112 and standard deviation equal to 4. Find the probability that the sample mean deviates from the population mean µ = 112 by no more than 3.Fifteen items or less: The number of customers in line at a supermarket express checkout counter is a random variable with the following probability distribution. X 0 1 2 3 4 5 P(x) 0.05 0.25 0.30 0.25 0.10 0.05 Send data to Excel
- The time taken by employees at Grace Floral shop to put a bouquet together has a normal distribution with mean 26.4 minutes and standard deviation .8 minutes. (i) Find the probability that an employee chosen at random takes between 24.6 and 27.8 minutes to put a bouquet together. [5] (ii) 12% of employees take more than t minutes to put a bouquet together. (ii) Find the value of t.Reaction time is the amount of time it takes to respond to a stimulus, and for automobile drivers, it is an important factor in staying safe while on the road by avoiding rear-end collisions. Reaction times vary from driver to driver and tend to be longer than one might think. A recent study determined that the time for an in-traffic driver to react to a brake signal from standard brake lights can be modeled with a normal distribution having mean value 1.24 seconds and standard deviation of 0.45 seconds. If we let X denote reaction time for automobile drivers, use the appropriate Normal Distribution to determine each of the following. 1. What is the probability that a driver has a reaction time less than 0.6 seconds? 2. Approximately what proportion of drivers have a reaction time more than 2.5 seconds? 3. Within what limits, centered about the mean, would you expect driver reaction times to lie with 95% probability? What are the z-scores for these limits? 4. What is the reaction time…A binomial distribution has p = 0.35 and n = 100. If we are trying to approximate its probability using a normal approximation (applying the Central Limit Theorem) what is the standard deviation that we will use for this approximation? (a) 0.4770 (b) 0.2275 (c) 0.0477 (d) 4.7697 (e) None of the above
- 5. Let x be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood) after a 12-hour fast. Assume that for people under 50 years old, x has a distribution that is approximately normal, with mean u = 85 and estimated standard deviation a = 25. A test result x< 40 is an indication of severe excess insulin, and medication is usually prescribed. (a) What is the probability that, on a single test, x < 40? That's find P(x < 40) (b) Suppose a doctor uses the average x fot two tests taken about a week apart. What is the probabilit that ( Hint: Your standard deviation here should be ) P(ĩ < 40)Women's heights are normally distributed with a mean given by u = 63.6 in. and a standard deviation given by o = 2.5 in. (a) If 1 woman is randomly selected, find the probability that her height is less than 62.6 in. Enter a number correct to 4 decimal places: (b) If 52 women are randomly selected, find the probability that they will have a mean height less than 62.6 in. Enter a number correct to 4 decimal places:Let the random variable X follow a standard normal distribution. If P(X < 70.75) = 0.75, what is 0.75 (a) 0.675 (b) 0.750 (c) 0.525 (d) 0.921 (e) None of the above
