Question

In: Statistics and Probability

Let be a continuous random variable that has a normal distribution with μ = 48 and...

Let be a continuous random variable that has a normal distribution with μ = 48 and σ = 8. Assuming , n/N ≤ 0.05, find the probability that the sample mean, x , for a random sample of 16 taken from this population will be more than 45.30 . Round your answer to four decimal places.

Solutions

Expert Solution

Solution :

Given that,

mean = = 48

standard deviation = = 8

n = 16

=   = 48

= / n = 8 / 16 = 2

P( > 45.30) = 1 - P( < 45.30)

= 1 - P[( - ) / < (45.30 - 48) / 2]

= 1 - P(z < -1.35)

Using z table,    

= 1 - 0.0885

= 0.9115

orchestra answered 2 years ago
Next > < Previous

Related Solutions

2] Let x be a continuous random variable that has a normal distribution with μ =...
2] Let x be a continuous random variable that has a normal distribution with μ = 48 and σ = 8 . Assuming n N ≤ 0.05 , find the probability that the sample mean, x ¯ , for a random sample of 16 taken from this population will be between 49.64 and 52.60 . Round your answer to four decimal places.
Let x be a continuous random variable that has a normal distribution with μ = 60...
Let x be a continuous random variable that has a normal distribution with μ = 60 and σ = 12. Assuming n ≤ 0.05N, where n = sample size and N = population size, find the probability that the sample mean, x¯, for a random sample of 24 taken from this population will be between 54.91 and 61.79. Let x be a continuous random variable that has a normal distribution with μ = 60 and σ = 12. Assuming n...
Let the random variable X follow a normal distribution with a mean of μ and a...
Let the random variable X follow a normal distribution with a mean of μ and a standard deviation of σ. Let 1 be the mean of a sample of 36 observations randomly chosen from this population, and 2 be the mean of a sample of 25 observations randomly chosen from the same population. a) How are 1 and 2 distributed? Write down the form of the density function and the corresponding parameters. b) Evaluate the statement: ?(?−0.2?< ?̅1 < ?+0.2?)<?(?−0.2?<...
Let X be a continuous random variable following normal distribution with mean value of: (a is...
Let X be a continuous random variable following normal distribution with mean value of: (a is 1) and standard deviation of b is 1/10 ,  What is the mode of X? (1 mark)  What is median of X? (1 mark)  What is ?(? > ?)? (1mark)  What is ?(? − ? < ? < ? + ?)? (1 mark)  What is ?(? − 1.96? < ? < ? + 1.96?))? (1mark)
Let X be a continuous random variable following normal distribution with mean value of: (a is...
Let X be a continuous random variable following normal distribution with mean value of: (a is the last digit of your student number) and standard deviation of b (b is the last digit of your student number divided by 10), a=9 b=9/10 What is the mode of X? What is median of X? What is P(X>a)? What is P(a-b<X<a+b)? What is P(a-1.96b<X<a+1.96b)?
1) Let   x be a continuous random variable that follows a normal distribution with a mean...
1) Let   x be a continuous random variable that follows a normal distribution with a mean of 321 and a standard deviation of 41. (a) Find the value of   x > 321 so that the area under the normal curve from 321 to x is 0.2224. Round your answer to the nearest integer. The value of   x is_______ (b) Find the value of x so that the area under the normal curve to the right of x is 0.3745. Round...
let the random variable x follow a normal distribution with μ = 50 and σ2 =...
let the random variable x follow a normal distribution with μ = 50 and σ2 = 64. a. find the probability that x is greater than 60. b. find the probability that x is greater than 35 and less than 62 . c. find the probability that x is less than 55. d. the probability is 0.2 that x is greater than what number? e. the probability is 0.05 that x is in the symmetric interval about the mean between...
Consider a continuous variable x that has a normal distribution with mean μ = 17.8 and...
Consider a continuous variable x that has a normal distribution with mean μ = 17.8 and standard deviation σ = 4.2. Answer the following questions. Approximate everything to 4 decimal places. P(x≤17)=P(x≤17)= P(x≥18)=P(x≥18)= P(15<x<19)= The value of x such that the area to your left under the normal curve is 0.3358 is: The value of x such that the area to your right under the normal curve is 0.2288 is: The 80th percentile is: Quartile 2 is:
Let X be a continuous random variable having a normal probability distribution with mean µ =...
Let X be a continuous random variable having a normal probability distribution with mean µ = 210 and standard deviation σ = 15. (a) Draw a sketch of the density function of X. (b) Find a value x∗ which cuts left tail of area 0.25 . (c) Find a value y∗ which cuts right tail of area 0.30. (d) Find a and b such that p(a ≤ X ≤ b) = 0.78.
Let z denote a random variable having a normal distribution with μ = 0 and σ...
Let z denote a random variable having a normal distribution with μ = 0 and σ = 1. Determine each of the probabilities below. (Round all answers to four decimal places.) (a) P(z < 0.2) =   (b) P(z < -0.2) =   (c) P(0.40 < z < 0.86) =   (d) P(-0.86 < z < -0.40) =   (e) P(-0.40 < z < 0.86) =   (f) P(z > -1.24) =   (g) P(z < -1.5 or z > 2.50) =
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT