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- Express the k th percentile, Pk , of a normally distributed variable in terms of its mean, µ, and standard deviation, σ.n=2485; p=0.63 find the standard deviation, o, for the binomial distribution which has the stated values of n and p.The systolic blood pressure (given in millimeters) of males has an approximately normal distribution with mean µ = 125 and standard deviation σ = 14. Systolic blood pressure for males follows a normal distribution. a. Calculate the z-scores for the male systolic blood pressures 102 and 149 millimeters. Round your answers to 2 decimal places. z-score for 102 millimeters: z-score for 149 millimeters: Find the probability that a randomly selected male has a systolic blood pressure between 102 and 149. Round your answer to 4 decimal places.
- The mean is μ = 15.2 and the standard deviation is σ = 0.9 Find the probability that X is greater than 15.2.Today, the waves are crashing onto the beach every 4.1 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 4.1 seconds. Round to 4 decimal places where possible. a. The mean of this distribution is b. The standard deviation is C. The probability that wave will crash onto the beach exactly 2.8 seconds after the person arrives is P(x = 2.8) = d. The probability that the wave will crash onto the beach between 0.4 and 1.9 seconds after the person arrives is P(0.4 0.82) = f. Suppose that the person has already been standing at the shoreline for 0.5 seconds without a wave crashing in. Find the probability that it will take between 1 and 4 seconds for the wave to crash onto the shoreline. g. 26% of the time a person will wait at least how long before the wave crashes in? seconds. h. Find the maximum for the lower quartile. seconds.The weight of a green forest frog has a normal distribution with mean 150.3 g and a standard deviation of 5g. Find the probability that a randomly selected frog weighs: i. Less than 153g ii. Between 150 g and 158 g
- Solve #22 using applications of normal distributionThe age of children in kindergarten on the first day of school is uniformly distributed between 4.91 and 5.97 years old. A first time kindergarten child is selected at random. Round answers to 4 decimal places if possible. a. The mean of this distribution is b. The standard deviation is c. The probability that the the child will be older than 5 years old?Write the formulae Given a normal distribution with mean of 12 & standard deviation of 2. What is the P (11 ≤ x ≤ 13)?
- A car battery's lifetime has an unknown distribution that is symmetric around its average of 800 days. The standard deviation of the lifetime is 50 days. Use Chebyshev's theorem to find an upper bound for the percentage of batteries that last shorter than 550 days? A. 5.56% B. 2.00% O C. 1.39% O D. 3.13%The mean is μ = 15 and the standard deviation is σ = 0.9.Find the probability that X is between 14.3 and 16.1.On average, indoor cats live to 12 years old with a standard deviation of 2.4 years. Suppose that the distribution is normal. Let X = the age at death of a randomly selected indoor cat. Round answers to 4 decimal places where possible. %3D a. What is the distribution of X? X N( b. Find the probability that an indoor cat dies when it is between 12.7 and 15.6 years old. c. The middle 50% of indoor cats' age of death lies between what two numbers? Low: years High: years Hint: