MATHEMATICS

  1. Assume that women’s heights are normally distributed with a mean given by μ=63.8 in,

and a standard deviation given by 2.5 inσ=2.5 in.

       If 15 women are randomly selected, find the probability that they have a mean height between 63.1
in and 64.1in. The probability is approximately_____.
  1. If 15 women are randomly selected, find the probability that they have a mean height between

 

63.163.1
and 64.1 in.

The probability is approximately_______

 

 

  1. A safety light is designed so that the times between flashes are normally distributed with a mean of

    3.00 s and a standard deviation of 0.70 s.
    a. Find the probability that an individual time is greater than 4.00 s.
    b. Find the probability that the mean for 60 randomly selected times is greater than 4.00 s.
    c. Given that the light is intended to help people see an obstruction, which result is more relevant for assessing the safety of the light?
    3. A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between
    46.0 and 56.0 minutes. Find the probability that a given class period runs less than 50.5 minutes.
      -Find the probability of selecting a class that run less than 50.5 minutes.
    4.A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between
    50.0and 60.0 minutes. Find the probability that a given class period runs between
    50.75 and 51.0 minutes.
    5. Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.

    –z=0.62 (the area shaded is to the left of 0.62)

  2. 6. Assume the readings on thermometers are normally distributed with a mean of 0degrees°C

and a standard deviation of 1.00degrees°C. Find the probability  P(z<−0.52 or z>0.52), where z is the reading in degrees.

 

P(z<−0.52 or z>0.52)equals=__________

 

7.Assume that adults have IQ scores that are normally distributed with a mean of

100 and a standard deviation
15.Find P9, which is the IQ score separating the bottom 99% from the top 91%.
   The IQ score that separates the bottom 99%from the top 91% is P9equals=_____
  1. Assume that adults have IQ scores that are normally distributed with a mean of
    100 and a standard deviation of 15. Find the third quartile Q3, which is the IQ score separating the top25% from the others.
     —The third quartile,Q3, is_______.
    9. A survey found that women’s heights are normally distributed with mean
    63.5 in and standard deviation 2.5 in. A branch of the military requires women’s heights to be between 58 in and 80 in.
    a. Find the percentage of women meeting the height requirement. Are many women being denied the opportunity to join this branch of the military because they are too short or too tall?
    b. If this branch of the military changes the height requirements so that all women are eligible except the shortest 1% and the tallest 2%, what are the new height requirements?
    10. Birth weights are normally distributed with a mean of
    3418 g and a standard deviation of 496 g. If a hospital plans to set up special observation conditions for the lightest 22% of babies, what weight is used for the cut-off separating the lightest
    22% from the others?
             The cut-off weight that separates the lightest 22%  of babies from the others is__________g.
  1. The lengths of pregnancies are normally distributed with a mean of 267 days and a standard deviation of 15
    days. a. Find the probability of a pregnancy lasting 308 days or longer. b. If the length of pregnancy is in the lowest 33%,
    then the baby is premature. Find the length that separates premature babies from those who are not premature.

 

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