Statistics and Probability Answers

The regulations of the board of health in a particular state specify that the fluoride level must not exceed 150 parts per million (ppm). The 25 measurements given here represent the fluoride levels for a sample of 25 days. Although fluoride levels are measured more than once per day, these data represent the early morning readings for the 25 days sampled.

75 86 84 85 97
94 84 83 83 89
88 77 76 76 82
72 105 94 94 83
81 97 93 93 79
a) Determine the range of the measurements.
b) Dividing the range by 7, the number of subintervals selected, and rounding, we have a class interval width of 5. Using 70.5 as the lower limit of the first interval, construct a frequency histogram and cumulative frequency curve.
c) Find the mean, median and standard deviation for the data set.
From the histogram constructed and also the measures of central tenency calculated, what can you conclude about the distribution of the data?

Question 2
A group of second year Forestry students conducted an experiment to compare the germination time (in days) for pine seeds sown in a green house with those sown outside the green house. Ten (10) seeds of pine were sown in the green house and ten (10) other seeds of pine were sown outside the green house. The number of days it took each seed to germinate was recorded and the following were the results.

Greenhouse 41 35 33 36 40 46 31 37 34 30
Outside 52 57 62 55 64 57 56 55 60 59

Calculate the mean, variance and standard error of the mean for each data set.

Test for equality of variances for the two data sets. Use α=0.10.
Do the data provide sufficient evidence to indicate that the mean germination time for seeds sown in the greenhouse was less than for seeds sown outside? Use α=0.05.

State three assumptions which are common for both tests conducted in b) and c).

The wages of a group of 5000 workers were found normally distributed with mean of rs800 & SD of rs200. Estimate %and number of workers getting wages above RS 700?

Given that 51.3% of all newly born children are boys;then what is the probability that in a sample of 5 newly born children;exactly 3 are boys

It is stated that 2 percent razor blades are defective out of 2000 random sample unit
1. 3 or more defective
2. 4 or less defective

Q. Find the variance and standard deviation of ungrouped data in which n=15,∑▒x=48, x ̅=10.

Two players A and B toss a coin alternately. A begins the game and the player who first throws heads is the winner. B's coin is fair but A's is biased and has probability 'p' of showing heads. Find the value of 'p' so that the game is equiprobable to both players.

Two players A and B toss a coin alternately. A begins the game and the player who first throws heads is the winner. B's coin is fair but A's is biased and has probability p of showing heads. The value of p so that the game is equiprobable to both players

In hypothesis testing solving:

It is claimed that the average weight of a bag of biscuits is 250 grams with a standard deviation 20.5 grams. Would you agree to this claim if random sample of 50 bags of biscuits showed a average weight of 240 grams, using a 0.05 evel of significance?

Suppose you just received a shipment of twelve televisions. Two of the televisions are defective. If two televisions are randomly​ selected, compute the probability that both televisions work. What is the probability at least one of the two televisions does not​ work?