Statistics and Probability Answers

(6.1.39) Assume that the readings on the thermometers are normally distributed with a mean of 0 and standard deviation of 1.00C. Assume ​2.7% of the thermometers are rejected because they have readings that are too high and another 2.7​% are rejected because they have readings that are too low. Draw a sketch and find the two readings that are cutoff values separating the rejected thermometers from the others.
The cutoff values are ? degrees.

(6.2.19) Suppose that the sitting​ back-to-knee length for a group of adults has a normal distribution with a mean of mu=23.6 in. and a standard deviation of alpha=1.2 in. These data are often used in the design of different​ seats, including aircraft​ seats, train​ seats, theater​ seats, and classroom seats. Instead of using 0.05 for identifying significant​ values, use the criteria that a value x is significantly high if​ P(x or ​greater)</=0.01 and a value is significantly low if​ P(x or ​less)</=0.01. Find the​ back-to-knee lengths separating significant values from those that are not significant. Using these​ criteria, is a​ back-to-knee length of 26.0 in. significantly​ high?
Find the​ back-to-knee lengths separating significant values from those that are not significant.
​Back-to-knee lengths greater than ? in. and less than ? in. are not​ significant, and values outside that range are considered significant.

(6.2.18) Assume that adults have IQ scores that are normally distributed with a mean of 101.2 and a standard deviation 20.7. Find the first quartile Q1​, which is the IQ score separating the bottom​ 25% from the top​ 75%. (Hint: Draw a​ graph.)
The first quartile is

A manufacturer of light bulbs finds that one light bulb model has a
mean life span of 1025 h with a standard deviation of 87 h. What percent of these
light bulbs will last?
a. at least 950 h?
b.
between 800 and 900 h?

An oil company conducts a geological study that indicates that an exploratory oil well in a certain
region should have 2r% chance of striking oil where r is the last three digits of your registration
number. If eight wells are drilled
a) What is the probability that the oil strikes in the third well?
b) What is the probability that oil strikes in at least five of the eight wells?
c) What is the mean value of not striking oil in a well?

: Write a script in R to remove the read counts with a row sum of 5 from the

following matrix. (12)

WT KI
0 1
50 20
30 30
3 6
3 8

1. The machineries company that supplies machinery to the ship John claims that their bridge equipment has a mean life of 54 months with a standard deviation of 10 months. Assume that the variable is normally distributed.
a. If 40 randomly selected bridge equipment will be test, what is the probability that a randomly selected equipment will last for less than 50 months?
b. If 40 randomly selected bridge equipment will be test, what is the probability that it will for more than 56 months?

John crewing agency has an average of 200 applicants per week for the position of deck cadet with a standard deviation of 12. A random sample of size 4 weeks will be taken.
A) determine the mean and standard error of the randomly selected weeks.
B) find the percentage of the randomly selected weeks to have a sample mean more than 210 applicants.
C) find the percentage of the randomly selected weeks to have a sample mean less than 185 applicants.
D) find the percentage of the randomly selected weeks to have a sample mean within 8 applicants of the population mean.

58
77
81
94
61
61
95
73
87
55
75
89
71
83
79
82
74
88
76
82
99
67
91
75
78


Use this data to construct a frequency table with an appropriate amount of intervals.

(b) Nine competitors in a beauty contest were given the following marks by three judges:

Competitors
Judges 1 2 3 4 5 6 7 8 9
A 56 54 65 69 72 74 77 88 54
B 65 78 62 74 55 82 66 64 82
C 64 79 68 71 82 73 81 84 81

Using the knowledge of ranking data, describe the pair of judges with nearest approach and the furthest approach to common tastes of beauty