Statistics and Probability Answers

ten students were intensive coaching in statistics. the score obtained in first and fifth test are given below. does the score from first test and fifth test show an improvement.test at 5% level of significance. given ftab 1.833
1st test 7 8 4 9 6 5 8 9 4 7
5th test 6 6 6 9 7 4 8 7 3 8

From a box containing 2 apples, 2 peaches and 2 oranges, 3 fruits are drawn at random. Let P be a random variable representing the number of oranges that occur. Construct a probability distribution.

A candy company has calibrated their machines to fill each bag of candy to an average weight of 505 grams with a standard deviation of 4 grams. The company tests the consistency of their machines by taking a sample of 25 bags and weighing them.



a- What is the probability that the average weight of candy bags in the sample is less than 503 grams?

b- What is the probability that the sample average is between 503 and 506?

c- Below what value do 95% of the sample means fall?

The manufacturer of the ColourSmart television claims that 85% of its sets last at least five years without needing a single repair. In order to test this claim, a consumer group randomly selected 400 consumers who have owned a ColourSmart television set for five years. Of these 400 consumers, 65 say that their ColourSmart television sets did need at least one repair.
Obtain the point estimate for the proportion of all ColourSmart television sets that have lasted at least five years without needing a single repair. (1M)
Determine whether the condition is satisfied to use the large sample formula (2M)

Find a 99% confidence interval for the true proportion of all ColourSmart television sets that have lasted at least five years without needing a single repair. (3M)

(6.4.18) A boat capsized and sank in a lake. Based on an assumption of a mean weight of 137lb, the boat was rated to carry 70 passengers​ (so the load limit was 9590​lb). After the boat​ sank, the assumed mean weight for similar boats was changed from 137lb to 174lb. Complete parts a and b below.
a. Assume that a similar boat is loaded with 70 ​passengers, and assume that the weights of people are normally distributed with a mean of 178.7lb and a standard deviation of 40.9lb. Find the probability that the boat is overloaded because the 70 passengers have a mean weight greater than 137lb.
The probability is?

(6.4.15) Suppose that an airline uses a seat width of 16.4 in. Assume men have hip breadths that are normally distributed with a mean of 14.1 in. and a standard deviation of 1.1 in.
Find the probability that if an individual man is randomly​ selected, his hip breadth will be greater than 16.4 in.
The probability is?

(6.4.13) A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of 183lb and a standard deviation of 40 lb. The gondola has a stated capacity of 25 ​passengers, and the gondola is rated for a load limit of 3500lb.
a. Given that the gondola is rated for a load limit of 3500​lb, what is the maximum mean weight of the passengers if the gondola is filled to the stated capacity of 25 ​passengers?
The maximum mean weight is ? lb.

(6.4.9) An elevator has a placard stating that the maximum capacity is 1240 lb 8 passengers.​ So, adult male passengers can have a mean weight of up to 1240/8=155 pounds. If the elevator is loaded with 8 adult male​ passengers, find the probability that it is overloaded because they have a mean weight greater than 155lb.​ (Assume that weights of males are normally distributed with a mean of 163 Ib and a standard deviation of 33 Ib​.) Does this elevator appear to be​ safe?
The probability the elevator is overloaded is

(6.4.7) Assume that females have pulse rates that are normally distributed with a mean of mu=76.0 beats per minute and a standard deviation of sigma=12.5 beats per minute.
a. If 1 adult female is randomly​ selected, find the probability that her pulse rate is between 72 beats per minute and 80 beats per minute.
The probability is

The overhead reach distances of adult females are normally distributed with a mean of 195 and a standard deviation of 8.3cm.
a. Find the probability that an individual distance is greater than 204.30 cm.
b. Find the probability that the mean for 15 randomly selected distances is greater than 193.20cm
c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30?