Statistics and Probability Answers

Suppose the weight of full-grown oranges in a citrus grove are normally distributed with a mean of 7.3 ounces and standard deviation of 2.1 ounces. Determine the probablity that 50 oranges randomly picked from the grove have a mean weight greater than 10.5 ounces.

Dr. Al Kali, an environmental chemist, measures the pH of numerous samples of water collected from a polluted lake. His data are normally distributed with a mean pH of 8.25 and a standard deviation of 0.35. What should Dr. Kali report as the margin of error for the 90% confidence interval for his data?

Solve this poblem:
Use the normal distribution to calculate the probability that a randomly selected new home in your state has an advertised selling price above $300,000. For estimates of μ and σ, use X-BAR and s. See your posting to the activity in Week 2's conference for the values of X-BAR and s.

Z=X-mean/standard deviation
z= 300,000-279,477.88/196,525.174


Specific requirements:

Please put the answer in the example format below:

Z=X-mean/standard deviation
z=300,000-698,411.50/950074.54

z= -0.419=.3372
1-.3372=0.6628
=66.28%

The waiting time in hours, W, of cars sent to a workshop is random with the following distribution f(w)=0.5e^-0.5w w>0. The profit, P, that the workshop makes is the following function of W:P=cN-8W where c is a constant and N is the number of cars waiting in the workshop. If there are 10 cars waiting, for what value of c will the expected profit be (i) positive (ii) More than $54.00?

There are 15 boys and 14 girls in a room. Two of
them are selected at random to take a survey. What is
the probability that the two people selected will be girls?

While driving, a motorist keeps track of both the number of traffic lights he encounters and the number ar which he is stopped. One week , he encounters 68 traffic lights and is stopped at 18 of them.
What is the probability he is stopped by the lights ? Probability as a decimal and a percent.

A researcher is interested in comparing the effectiveness of three different kinds of therapy for anger problems. Eight participants are randomly assigned to three treatment conditions: Cognitive Therapy (CT), Cognitive-Behavioral Therapy (CBT), and Interpersonal Therapy (IT). All participants complete the weekly treatment for 8 weeks. Participants take an anger test before and after the 8-week treatments. Each participant’s difference score (= anger score after the treatment minus (–) anger score before the treatment) is shown in the following table. The three therapists in this experiment have equal educational levels and clinical experiences.
CT CBT IT
3 5 7
4 4 8
4 6 9
4 6 10
3 5 6
8 4 7
6 9 11
2 7 10
a. What statistical test should be used to analyze the data?
b. Identify H0 and Ha for this study.
c. Conduct the appropriate analysis.
d. Should H0 be rejected? What should the researcher conclude?

The US average BMI for men is 26.2 and is normally distributed with a standard devation of 1.23. Use the sample data to test the claim that men in Minnesota have a lower BMI than the average US male. a=.05

What is the present value of a maturity value of $2,484 bearing interest at 14% for 90days? Use formula P=M/1 + rt

Let x represent the life of a 60-watt light bulb. The x distribution has a mean of 1000 hours with standard deviation of 75 hours. Convert each of the following z intervals to x intervals.

(a) z > 1.25

(b) -1.5 > z > 2.4

(c) z > 2.25