The average precipitation for the first 7 months of the year is 19.32 inches with standard deviation of 2.4 inches. Assume that the average precipitation is normally distributed. What is the probability that a randomly selected year will have precipitation greater than 18 inches for the first 7 months.

Q: If the daily wage of a worker in a large factory has an average of 180 usd, the standard deviation…

A: Given: mean: 180 usd, standard deviation: 5 usd, n = 75.The required probability is…

Q: the average age of ceos is 54 years. assume the random variable is normally distributed. if the…

A: Let X be the random variable from normal distribution with mean (μ) = 54 and standard deviation (σ)…

Q: A lightbulb is advertised as lasting 1000 hours with a standard deviation of 150 hours. Assume the…

A: The lasting duration of lightbulb is normally distributed with mean 1000 hours and standard…

Q: The height of the students in a class shows normal distribution. Students in this class have an…

A: We have to find givén probability..

Q: The time spent waiting in the line is approximately normally distributed. The mean waiting time is 5…

A: According to the given information, we have Mean = 5 minutes Standard deviation = 1 minutes

Q: The amount of snowfall falling in a certain mountain range is normally distributed with an average…

A: From the provided information, Mean (µ) = 170 inches Standard deviation (σ) = 20 inches X~N (170,…

Q: If a female is randomly selected, find the probability that her pulse rate is between 69 beats per…

A:

Q: Tiger Woods hits an average driver 287.2 yards with a standard deviation of 24.6 yards. What is the…

A: The probability value is calculate by means of standard normal variate with the random variable,…

Q: The life of a vacuum cleaner is normally distributed with mean of 2 years and a standard deviation…

A: Given: Mean(μ)  = 2 years Standard deviation (σ) = 1 years

Q: A Run is a 5 kilometer race. The time taken for each runner to complete the race was recorded and…

A: A Run is a 5 kilometer race.Mean Time =28 MinutesStandard deviation =5 Minutes We have to find the…

Q: The average number of miles driven on a full tank of gas in a certain model car before its​ low-fuel…

A: It is given that the mean is 399 and the standard deviation is 36.

Q: On the Gulf Freeway at 7:00 AM, the average travel time from Beltway 8 to Downtown is 29.5 minutes…

A: We have given that the random variable X i.e. travel time is normally distributed with average(mean)…

Q: The time it takes to drive through the middle of campus follows a uniform distribution with a…

A:

Q: 5. The average American adult eats an average of 6.5 gallons of ice cream per year. Assume the…

A: (5) X follows a Normal distribution with mean = 6.5 and S.D = 2.3 Then z=(x-mean)/SD =…

Q: The time spent waiting in the line is approximately normally distributed. The mean waiting time is 6…

A: Mean=M=6, Standard deviation=S=3X~N(M=6, S=3)

Q: A​ bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean…

A: It is given that the ratings are normally distributed with mean 200 miles and standard deviation 50.

Q: the amount of snowfall falling in a certain mountain range is normally distributed with a mean of 88…

A: It is given that the normal distribution has a mean, μ=88 and the standard deviation, σ=16. The…

Q: The amount of snowfall falling in a certain mountain range is normally distributed with 80 inches…

A: Let x¯ denotes the mean annual snow falling during 25 randomly picked years. The mean is 80, and…

Q: annual precipitation amounts in a certain mountain range are normally distributed with a mean of 82…

A: Given,sample size(n)=25mean(μ)=82standard deviation(σ)=9

Q: The time spent waiting in the line is approximately normally distributed. The mean waiting time is 7…

A:

Q: Assume IQ scores for adults are normally distributed with a mean of 100 and a standard deviation of…

A:

Q: Body temperatures of adults are normally distributed with a mean of 98.60 Fahrenheit and a standard…

A: The Z-value of a random variable X is defined as follows: Here, the mean and standard deviation of…

Q: The time spent waiting in the line is approximately normally distributed. The mean waiting time is 5…

A: Here, mean is 5 and standard deviation is 3. We will use z-standard normal distribution.

Q: Brenda has collected data to find that the finishing times for cyclists in a race has a normal…

A: Given the finishing time for cyclists in a race has normal distribution with mean 143 minutes and…

Q: The green turtle migrates across the Southern Atlantic in the winter, swimming great distances. A…

A: X~N( μ , ?)   μ=2200 , ?=625   Z-score =( x - μ )/?

Q: The height of 10 year old females is normally distributed with a mean of 54.8 inches and a standard…

A: It is given that mean and standard deviation are 54.8 inches and 2.74 inches, respectively.

Q: The time spent waiting in the line is approximately normally distributed. The mean waiting time is…

A:

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!