# Normal Probability Distribution and Confidence Intervals

What is the probability of P(-1.4 < Z < 0.6)?

In a standard normal distribution, what is the area which lies between Z = -1.72 and

Z = 2.53?

Use the following information to conduct the confidence intervals specified to estimate μ.

95% confidence; X ̅=25, σ^2= 12.25, and n=60.

30% confidence; X ̅=119.6, S^2= 570.7321, and n=75

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#### Solution Preview

Hi there,

P(-1.4<z<0.6)=P(z<0.6)-P(z<-1.4)=0.7257-0.0808=0.6449

area which lies between z=-1.72 and z=2.53: ...

Population mean, sample size, sample mean

1. An upper-level sociology class at a large urban university has 120 students, including 34 seniors, 57 juniors, 22 sophomores and 7 freshmen.

a). Imagine that you choose one random student from the classroom (perhaps by using a random number table). What is the probability that the student will be junior?

b). What is the probability that the student will be freshman?

c). If you are asked to select a proportionate stratified sample of 30 from the classroom, stratified by class level (senior, junior and so on), how many students from each group will be sample?

d). If instead you are to select a disproportionate sample of size 20 from the classroom, with equal numbers of students from each class level in the sample, how many freshmen will be in the sample.

2. For the total population of a large southern city, mean family income is $34,000, with a standard deviation (for the population) of 5, 000.

a). Imagine that you take a subsample of 200 city residents. What is the probability that your sample mean is between $33,000 and $34,000?

b). For this same sample size, what is the probability that the sample mean exceeds $37,000?

3. The police department in your city was asked by the mayor?s office to estimate the cost of crime. The police began their study with burglary records, taking a random sample of 500 files since there were too many crime records to calculate statistics for all the crimes committed.

a). If the average dollar loss in burglary, for this sample of size 500, is $678, with a standard deviation of $560, construct the 95% confidence interval for the true average dollar loss in burglaries?

b). An assistant to the mayor, who claims to understand statistics, complaints about your confidence interval calculation. She asserts that the dollars losses from burglaries are not normally distributed, which in turn makes the confidence interval calculation meaningless. Assume that she is correct about the distribution of money loss. Does that imply that the calculation of confidence interval is not appropriate? Why or why not?