Problem:1 Suppose that x is normally distributed random variable with µ = 11 and variance = 4. Find each of the following:
a)P(10<x <12)
b)P(x > 13.24)
c)P(x < x0) 0.75 find Xo

A sample with n = 50 provides a sample mean of 9.46 and sample standard deviation of 2. At alpha = 0.05, what is the critical value for z or t? What is the rejection rule?

Solution Preview

Note : Please see the attached file. Work done in equation editor may be missing or may not properly print here.

Suppose that x is normally distributed random variable with µ = 11 and σ2 = 4. Find each of the following:

a) P(10≤ x ≤12)

.
Let us find Z for X=10, and X=12. Z is given by

For X=10,

Negative sign implies that value of X lies in left side of mean.

From the tables we get Corresponding value of Probability = 0.1915

For X=12,
Positive sign implies that value of X lies in right side of mean.

From the tables we get Corresponding value of Probability = 0.1915

For ...

Solution Summary

Solution explains the steps in finding probability for different values of X. X is normally distributed.
Second problem is about hypothesis testing for normal distribution. Critical Value of Z and rejection rule have been worked out.

Finding Probability and Sample size using Normally Distributed Sample ... Florida at the end of trading each day for the last year followed the normal distribution. ...

... b) Find the probability that this shipment is not accepted if 10% of this shipment is defective. ...Find the following probabilities: a) P(x < 74.0) b) P ...

... week we learned about normal distributions: a. Using ... a normal distribution and a standard normal distribution. ... convert values to z scores to find probability? ...

... b. Find a 99% confidence interval estimate of the mean ... The expert examines probability, normal distributions, and binomial probabilities for randomly ...

... spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, find the probability that a ...

... 1)=P(-1/sqrt(10.16/3)<Z<1/sqrt(10.16/3))=P(-0.54<Z<0.54)=0.4108 from normal table. ... D) For each of the possible sample sizes find the probability that the ...

... e. Based on the probability found in the previous part ... is selected, what is the probability that the ... on the topic of normal distribution, sampling distribution...

... Assume that this distribution is normal. 1. Find the probability that a particular family of four selected at random spends between $150 and $200? ...

... that is find the z-score corresponding to ... percentages of the standard normal distributions are determined ... random variable x 's probability distribution, where ...