# Te speeds of two types of drones in reaching a target from the same distance are compared. Te owner.

Te speeds of two types of drones in reaching a target from
the same distance are compared. Te owner of drone A claims that it reaches the
target faster than drone B from the other type. Te speeds are measured 5 times
from the same distance. Let X be the number of times that drone A reached the
target faster than drone B. When the rejection region is { 5 X = }, answer the
following questions:

a. If the probability that drone A is faster than drone B is
p,  fnd the distribution of X.

b. State the testing hypotheses.

c. Find the probability of a type I error.

d. When the
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Te speeds of two types of drones in reaching a target from
the same distance are compared. Te owner of drone A claims that it reaches the
target faster than drone B from the other type. Te speeds are measured 5 times
from the same distance. Let X be the number of times that drone A reached the
target faster than drone B. When the rejection region is { 5 X = }, answer the
following questions:

a. If the probability that drone A is faster than drone B is
p,  fnd the distribution of X.

b. State the testing hypotheses.

c. Find the probability of a type I error.

d. When the probability that drone A is faster in reaching
the target than drone B is 90%, fnd the power of the test.

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