probability Archives - Page 3 of 23

Normal Probability Distribution

The amount of syrup that people put on their pancakes is normally distributed with a mean of 65 mL and standard deviation of 12 mL. Suppose that 55 randomly selected people are observed pouring syrup on their pancakes. Round all answers to 4 decimal places where possible.

(a) What is the distribution of X? X ~ N(,)(b) What is the distribution of x̄? x̄ ~ N(,)(c) If a single randomly selected individual is observed, find the probability that the amount of syrup this person consumes is between…

Normal Probability Distribution

Find the value of z such that 0.13 of the area lies to the left of z.

Answer : Given information : The area lies to the left of z =0.13 The value of z : Solution : The area lies to the left of z : $P (x < z) = 0.13$ $∴ z = - 1.126$

Normal Probability Distribution

The amount of syrup that people put on their pancakes is normally distributed with a mean of 50 mL and standard deviation of 9 mL. Suppose that 52 randomly selected people are observed pouring syrup on their pancakes. Round all answers to 4 decimal places where possible.

Normal Probability Distribution

It is known that the average national IQ (Intelligent Quotient) is about 109 with standard deviation 13. Assuming that the population of all IQ’s is normally distributed, find the probability that 20 randomly selected people will have an average IQ that is greater than 119.

Answer : Given information : The population mean $(μ) = 109$ The population standard deviation $(σ) = 13$ The sample size $(n) = 20$ Solution : → The probability that 20 randomly selected people will have an average IQ that…

Binomial Probability Distribution

Thirty-nine percent of U.S. adults have very little confidence in newspapers. You randomly select ten U.S. adults. Find the probability that the number who have very little confidence in newspapers is (1) exactly three.

Answer : Given information : Probability of success $(p) = 0.39$ Sample size $(n) = 10$ Solution : → The probability exactly three : $P (x = 3) = (\binom{n}{x}) \cdot p^{x} \cdot (1 - p)^{n - x}$ $$= \binom{10}{3} \cdot 0.39^3 \cdot (1 –…

Binomial Probability Distribution

Thirty-nine percent of U.S. adults have very little confidence in newspapers. You randomly select ten U.S. adults. Find the probability that the number who have very little confidence in newspapers is (a) exactly six

(a) The probability that the number who have very little confidence in newspapers is exactly six is _____. Answer : Given information : Probability of success $(p) = 0.39$ Sample size $(n) = 10$ Solution : → The probability that…

Normal Probability Distribution

The amount of syrup that people put on their pancakes is normally distributed with a mean of 55 mL and standard deviation of 11 mL. Suppose that 45 randomly selected people are observed pouring syrup on their pancakes. Round all answers to 4 decimal places where possible.

Normal Probability Distribution

Solve the equation z = (x – μ) / σ for μ, when z = 1.54, x = 37.4, and σ = 2.

Answer : Given information : The z-score =1.54 The population standard deviation $(σ) = 2$ Solution : → The population mean $(μ)$ : $∴ z = \frac{X - μ}{σ}$ $∴ 1.54 = \frac{37.4 - μ}{2}$ $$\therefore \mu =…

Normal Probability Distribution

The amount of syrup that people put on their pancakes is normally distributed with a mean of 60 mL and standard deviation of 12 mL. Suppose that 50 randomly selected people are observed pouring syrup on their pancakes. Round all answers to 4 decimal places where possible.

Blog Normal Probability Distribution

The amount of syrup that people put on their pancakes is normally distributed with mean 55 mL and standard deviation 10 mL. Suppose that 47 randomly selected people are observed pouring syrup on their pancakes. Round all answers to 4 decimal places where possible.