) Picture frames are produced such that the four sides of a picture frame consist of two pieces from a population whose mean length is 32 cm and whose standard deviation is 0.2 cm and two pieces selected from a population whose mean length is 44 cm and whose standard deviation is 0.1 cm.
Find the mean perimeter of frame

The mean perimeter of frame = 38 cm

Step-by-step explanation:

By perimeter of a rectangle, the formula is given as:

Perimeter of rectangle = 2(A + B)

Going by the illustration in the question, the perimeter is

==> 2(32 + 44) = 152 cm.

However, we a given the mean perimeter of the frame which are:

32 and 44. We can either choose to say; each sides is (32 by 32) and (44 by 44). Or we consider it in mean/average term as given: (32 by 44).

Case 1: To obtain the mean perimeter of the frame using the first scenario, we say:

Mean perimeter = (32+32+44+44)/4 = 38 cm.

Case 2: We can simply say:

Mean perimeter = (32 + 44)/2 = 38 cm.

Graphically: Assuming that the frame is given below

                     32 cm

         |                                      |

         |                                      |

44 cm|                                      | 44 cm

         |                                      |

         |                                      |

         |                                      |

                       32 cm

The mean of upper frame/bars = 32 cm

The mean of side frame/bars  =  44 cm

Hence, the mean of the perimeter = (32 + 44)/2 = 38 cm

OR,

we take the sum of all the sides (32 + 44 + 32 + 44) and divide by total number of sides (4). That is;

The mean of the perimeter = (32 + 44 + 32 + 44)/4 = 38 cm

the answer is 62.8 cubic units