Statistics and Probability Answers

A cement manufacturer claims that the average weight of his product is 40 kg: with a standard deviation of 2.35 kg A sample of 45 bags was taken and found to have a mean weight of 38.71 kg: Are we going to accept the claim of the cement manufacturer? Use 0.01 level of significance

1.     In a Harris poll of 630 human resource professionals, 38.4 % said that they had at least one child by the age of 30 years.

a. Among the 630 professionals who were surveyed, how many of them said they had at least one child before 30 years of age.

b. Construct a 99% confidence interval estimate for the proportion of all human resource professionals with at least one child before 30 years of age.

c. Repeat part (b) using a confidence interval level of 90%.

d. Compare the confidence intervals from part (b) and (c) and identify the interval that is wider. Why is it wider?

1.     A particular brand of petrol was used in 80 randomly chosen cars of the same model and age. The petrol consumption, x miles per gallon, was obtained for each car. The results are summarized by

∑x=1896 and ∑x²=45959.

Calculate a 99% confidence interval for the mean petrol consumption of all cars of this model and age.

A student taking up Statistics is analyzing the scores in Mathematics of the students in Grade 8 - Turquoise. He wants to know whether the mean score of the 25 students in 8-Turquoise is better or not than the mean score of all the students taking up Grade 8 Math in the entire school. The mean score of all the students taking up Grade 8 Math is 89. The mean and standard deviation of the scores of the students in 8 - Turquoise is 95 and 15, respectively. Assume a 95% confidence level and that the scores of all the students in Grade 8 Math follow a normal distribution.

Supposed 25 respondents were selected from a normal population with a mean of 12.5.

If the sample has a mean of 15.4 and standard deviation of 3, what percentile does the

sample mean represent?

Jon for the

The blood groups of 200 people are distributed as follows: 40 have type A blood, 75 have type B blood, 60 have type O blood, and 25 have type AB blood. If a person from any of the group is selected at random, what is the probability that this person has an O blood type? How about the AB blood type?

According to Chemical Engineering Progress (Nov. 1990), approximately 30% of all pipework failures in chemical plants are caused by operator error.

(a) What is the probability that out of the next 20 pipework failures at least 10 are due to operator error?

(b) What is the probability that no more than 4 out of 20 such failures are due to operator error?

(c) Suppose, for a particular plant, that, out of the random sample of 20 such failures, exactly 5 are operational errors.

Do you feel that the 30% figure stated above applies to this plant? Comment.

In February 2021, 1664,479 person's took covid vaccine in Asia. The distribution of Pfizer vaccine has a n= 496 and o= 144. Find Z if x= 366

an electrical company claims that an average life of bulbs it manufactures is 1200 hours with standard deviation of 250 hours.If a random sample of 100 bulbs is chosen, what is the probability of the sample mean will be:

a.Greater than 1150 hours?

b.Less than 1250 hours?

c.Between 1150 and 1250 hours?​