Statistics and Probability Answers

Subjective wellbeing was measured among a sample of Statistics students with M=150 and S squared=25. Determine the z-scores for the students who obtained the following scores on the subjective wellbeing measure.

a) 110

b) 135

 Given a mean score of 43 and a standard deviation of 5 for ‘Teaching readiness test’ among a sample of PGCE students from Cornerstone, calculate raw scores for the following;

1. A normal distribution has u=80 and o=10. What is the probability of randomly selecting the following scores?

a) x > 75

b) x < 85

c) between the mean and a score of 90

d) between the mean and a score of 50

e) 75 < x < 85

Show all calculations

2. Determine the z-score value in each of the following scenarios:

a) what z-score value separates the top 8% of a normal distribution from the bottom 92%?

b) what z-score value separates the top 72% of a normal distribution from the bottom 28%?

c) what z-scores values represents the middle 90% of the values in a normal distribution?

Show all calculations

The score obtained on an emotional intelligence test is normally distributed, with an average score (μ) of 115 and a standard deviation (σ) of 9.5. What is the probability that a randomly selected person will: Q.1.3.1 Obtain a score between 110 and 118? Interpret your answer. (5) Q.1.3.2 Obtain a score between 109 and 113? Interpret your answer. (5)

It has been found that 1 out of every 20 people who visit a retail website make a purchase worth R500 or more. If we randomly select a sample of 15 visitors to the website, what is the probability that no more than three of the visitors will make a purchase worth R500 or more? Interpret your answer.

A secretary makes 6 errors per page on the average. What is the probability that on next page she makes:

(c) At most 5 errors?

(d)Between 5 and 8 errors?A secretary makes 6 errors per page on the average. What is the probability that on next page she makes:

(a) 4 or more errors?

(b) No errors?

(c) At most 5 errors?

(d)Between 5 and 8 errors?

A manufacturer of cotton pins knows that 5 percent of his product is

defective. If he sells cotter pins in boxes of 100, and guarantee that not more than 4

pins will be defective, what is the approximate probability that a box will, fail to

meet the guaranteed quality.

b) Which distribution is used in (a)also give the reason .

According to the U.S. Bureau of Labor Statistics, the average weekly earnings of a production worker in 1997 were $421.20. Suppose a labor wants to test to determine whether this figure is still accurate today. The researcher randomly selects 60 production workers from across the United States and obtains a representative earning statement for one week from each. The resulting sample average is $435.70. Assuming a population standard deviation of $33, and a 5% level of significance, determine whether the mean weekly earning of a population worker has changed.

Show that Tn=X+1/n+1 is a consistent estimator of the parameter theta of a binomial population

The sales of a small factory since 2008 are as follows:

Year Sales (in ₹ lakhs)

• 2008 8
• 2009 10
• 2010 9
• 2011 11
• 2012 11
• 2013 12

Using 2008 as the zero year, find the least-square trend-line equation.