A survey found that women's heights are normally distributed with mean 64.2 in. and standard deviation 4.2 in. The survey also found that men's heights are normally distributed with mean 70.1 in. and standard deviation 4.1 in. Most of the live characters employed at an amusement park have height requirements of a minimum of 57 in. and a maximum of 63 in. Complete parts (a) and (b) below

A survey found that women's heights are normally distributed with mean 64.2 in. and standard deviation 4.2 in. The survey also found that men's heights are normally distributed with mean 70.1 in. and standard deviation 4.1 in. Most of the live characters employed at an amusement park have height requirements of a minimum of 57 in. and a maximum of 63 in. Complete parts (a) and (b) below

a) find the percentage of women meeting the height requirement

b) find the percentage of men meeting the height requirement

a

P(57 <  X <  63) = 34.4%

b

P(57 <  X <  63) =  4.096%

Step-by-step explanation:

From the question we are told that

    The mean of women's height is

    The standard deviation is

     The mean of men' height is

     The standard deviation of men's height is

      The minimum height requirement is  a =  57 in

      The maximum height requirement is  b = 63 in

Generally the percentage of women meeting the height requirement  is mathematically represented as

So

=>  

Generally from the z table the probability of  ( Z <-0.2857)  and  (Z <  -1.7143) is  

    P( Z <-0.2857)   =  0.38755

 and

    P(Z <  -1.7143) =  0.043237

So

   P(57 <  X <  63) = 0.38755  - 0.043237

=>  P(57 <  X <  63) = 0.3443

Converting to percentage

     P(57 <  X <  63) = 0.3443  * 100 =  34.4%

Generally the percentage of men meeting the height requirement  is mathematically represented as

So

      P(57 <  X <  63) = P( -3.1951  < Z <-1.7317)

=>  

Generally from the z table the probability of  ( Z <-0.2857)  and  (Z <  -1.7143) is  

    P( Z <-1.7317)   =  0.041663

 and

    P(Z <  -3.1951 ) =  0.00069891

So

   P(57 <  X <  63) = 0.041663  - 0.00069891

=>  P(57 <  X <  63) = 0.04096

Converting to percentage

     P(57 <  X <  63) = 0.04096   * 100 =  4.096%

0.32

step-by-step explanation:

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