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Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.
Assume that thermometer readings are normally distributed with a mean of 0 °C
and a standard deviation of 1.00 °C. A thermometer is randomly selected and tested. For the case below, draw a sketch, and find the probability of the reading. (The given values are in Celsius degrees.)
Find the area of the shaded region. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.
Assume that adults have IQ scores that are normally distributed with a mean of μ100= and a standard deviation σ=20. Find the probability that a randomly selected adult has an IQ between 87 and 113.
The probability that a randomly selected adult has an IQ between 87 and 113 is?
(Show work)
Where would a value separating the top 15% from the other values on the graph of a normal distribution be found?
Choose the correct answer below.
the right side of the horizontal scale of the graph
the center of the horizontal scale of the graph
on the top of the curve
the left side of the horizontal scale of the graph
The population of current statistics students has ages with mean μ and standard deviation σ.
Samples of statistics students are randomly selected so that there are exactly 55 students in each sample. For each sample, the mean age is computed. What does the central limit theorem tell us about the distribution of those mean ages?
Choose the correct answer below.
Because n>30, the sampling distribution of the mean ages is precisely a normal distribution with mean μ and standard deviation σ/ √55
Because n>30, the sampling distribution of the mean ages can be approximated by a normal distribution with mean μ and standard deviation σ.
Because n>30, the sampling distribution of the mean ages can be approximated by a normal distribution with mean μ and standard deviation σ/ √55
Because n>30, the central limit theorem does not apply in this situation.
Fill in the blank.
_____________ is the distribution of all values of the statistic when all possible samples of the same size n are taken from the same population.
The sampling distribution of a statistic
The standard normal distribution
The uniform distribution
The normal distribution
An airliner carries 50 passengers and has doors with a height of 75 in. Heights of men are normally distributed with a mean of 69.0 in and a standard deviation of 2.8 in. Complete parts (a) through (d).
a. If a male passenger is randomly selected, find the probability that he can fit through the doorway without bending.
The probability is ?
b. If half of the 50 passengers are men, find the probability that the mean height of the
25 men is less than 75 in.
c. When considering the comfort and safety of passengers, which result is more relevant: the probability from part (a) or the probability from part (b)? Why?
The probability from part (a) is more relevant because it shows the proportion of male passengers that will not need to bend.
The probability from part (b) is more relevant because it shows the proportion of male passengers that will not need to bend.
The probability from part (a) is more relevant because it shows the proportion of flights where the mean height of the male passengers will be less than the door height.
The probability from part (b) is more relevant because it shows the proportion of flights where the mean height of the male passengers will be less than the door height.
d. When considering the comfort and safety of passengers, why are women ignored in this case?
Since men are generally taller than women, it is more difficult for them to bend when entering the aircraft. Therefore, it is more important that men not have to bend than it is important that women not have to bend.
There is no adequate reason to ignore women. A separate statistical analysis should be carried out for the case of women.
Since men are generally taller than women, a design that accommodates a suitable proportion of men will necessarily accommodate a greater proportion of women.
Which of the following is NOT a requirement for using the normal distribution as an approximation to the binomial distribution?
Choose the correct answer below.
The sample is the result of conducting several dependent trials of an experiment in which the probability of success is p.
n≥5
The sample is a simple random sample of size n from a population in which the proportion of successes is p, or the sample is the result of conducting n independent trials of a binomial experiment in which the probability of success is p.
n≥5
If n≥5 and n≥5, estimate P (more than 7) with n=11 and p=0.4 by using the normal distribution as an approximation to the binomial distribution; if n<5 or n<5, then state that the normal approximation is not suitable.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
P (more than 7) =
(Round to four decimal places as needed.)
The normal distribution cannot be used.
