Question

In: Statistics and Probability

Assume that? women's heights are normally distributed with a mean given by mu equals 64.6 in?,...

Assume that? women's heights are normally distributed with a mean given by mu equals 64.6 in?, and a standard deviation given by sigma equals 1.9 in. ?(a) If 1 woman is randomly? selected, find the probability that her height is less than 65 in. ?(b) If 50 women are randomly? selected, find the probability that they have a mean height less than 65 in. ?(?a) The probability is approximately nothing. ?(Round to four decimal places as? needed.) ?(b) The probability is approximately nothing. ?(Round to four decimal places as? needed.)

Solutions

Expert Solution

Solution:

Given that,

mean = = 64.6

standard deviation = = 1.9

A ) p ( x < 65 )

= p ( x -  / ) < ( 65 - 64.6 / 1.9 )

= p ( z < 0.4 / 1.9 )

= p ( z < 0.21)

Using z table

= 0.5832

Probability = 0.5832

B ) n = 50

So,

   = 64.6

=  ( /n) = (1.9 / 50 ) = 0.2687

p ( < 65 )

= p ( -  / ) < ( 65 - 64.6 / 0.2687 )

= p ( z < 0.4 / 0.2687 )

= p ( z < 1.49)

Using z table

= 0.9319

Probability = 0.9319


Related Solutions

Assume that​ women's heights are normally distributed with a mean given by mu equals 63.4 in​,...
Assume that​ women's heights are normally distributed with a mean given by mu equals 63.4 in​, and a standard deviation given by sigma equals 1.9 in. ​(a) If 1 woman is randomly​ selected, find the probability that her height is less than 64 in. ​(b) If 31 women are randomly​ selected, find the probability that they have a mean height less than 64 in.
Assume that​ women's heights are normally distributed with a mean given by mu equals 64.4 in...
Assume that​ women's heights are normally distributed with a mean given by mu equals 64.4 in and a standard deviation given by sigma equals 2.9 in (a) If 1 woman is randomly​ selected, find the probability that her height is less than 65 in. ​(b) If 45 women are randomly​ selected, find the probability that they have a mean height less than 65
Assume that​ women's heights are normally distributed with a mean given by mu equals 62.1 in​,...
Assume that​ women's heights are normally distributed with a mean given by mu equals 62.1 in​, and a standard deviation given by sigma equals 2.7 in. ​(a) If 1 woman is randomly​ selected, find the probability that her height is less than 63 in. ​(b) If 32 women are randomly​ selected, find the probability that they have a mean height less than 63 in.
Assume that​ women's heights are normally distributed with a mean given by mu equals 62.2 in​,...
Assume that​ women's heights are normally distributed with a mean given by mu equals 62.2 in​, and a standard deviation given by sigma equals 1.9 in. Complete parts a and b. a. If 1 woman is randomly​ selected, find the probability that her height is between 61.9 in and 62.9 in. The probability is approximately nothing. ​(Round to four decimal places as​ needed.) b. If 14 women are randomly​ selected, find the probability that they have a mean height between...
Assume that women's heights are normally distributed with a mean given by mu equals 63.3 inμ=63.3...
Assume that women's heights are normally distributed with a mean given by mu equals 63.3 inμ=63.3 in , and a standard deviation given by sigma equals 2.8 inσ=2.8 in. (a) If 1 woman is randomly selected, find the probability that her height is less than 6464 in. (b) If 3737 women are randomly selected, find the probability that they have a mean height less than 6464 in.
Assume that​ women's heights are normally distributed with a mean given by mu equals 62.6 inμ=62.6...
Assume that​ women's heights are normally distributed with a mean given by mu equals 62.6 inμ=62.6 in​, and a standard deviation given by sigma equals 2.2 inσ=2.2 in. ​(a) If 1 woman is randomly​ selected, find the probability that her height is less than 6363 in.​ (b) If 3232 women are randomly​ selected, find the probability that they have a mean height less than 6363 in.
Assume that​ women's heights are normally distributed with a mean given by mu=64.4 in ​, and...
Assume that​ women's heights are normally distributed with a mean given by mu=64.4 in ​, and a standard deviation given by sigma=1.8 in . Complete parts a and b. a. If 1 woman is randomly​ selected, find the probability that her height is between 64.2 in and 65.2 in. The probability is approximately ? . ​(Round to four decimal places as​ needed.) b. If 14 women are randomly​ selected, find the probability that they have a mean height between 64.2...
assume that women's heights are normally distributed with a mean 64.6 in. and a standard deviation...
assume that women's heights are normally distributed with a mean 64.6 in. and a standard deviation 2.6 in. if 49 women are randomly selected, find the probability they have a mean less than 65 in
Assume that​ women's heights are normally distributed with a mean given by ​, 62.6 and a...
Assume that​ women's heights are normally distributed with a mean given by ​, 62.6 and a standard deviation given by 2.8 . ​(a) If 1 woman is randomly​ selected, find the probability that her height is less than 63 in. ​(b) If 49 women are randomly​ selected, find the probability that they have a mean height less than 63 in.
Assume that​ women's heights are normally distributed with a mean given by μ=63.5 in​, and a...
Assume that​ women's heights are normally distributed with a mean given by μ=63.5 in​, and a standard deviation given by σ=2.1 in. ​(a) If 1 woman is randomly​ selected, find the probability that her height is less than 64 in. ​(b) If 44 women are randomly​ selected, find the probability that they have a mean height less than 64
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT