Question

According to a government study among adults in the 25 0 to 34-year age group, the mean amount spent per year on reading and entertainment is $2,035. Assume that the distribution of the amounts spent follows the normal distribution with a standard deviation of $601. a) a) What percent of the adults spend more than $2,475 per year on reading and entertainment? b) b) What percent spend between $2,475 and $3,150 per year on reading and entertainment? c)   What percent spend less than $1,025 per year on reading and entertainment?

Answer 1

ANSWER::

(a) What percent of the adults spend more than $2,475 per year on reading and entertainment?

P(X>2475 ) = P((X-mean)/s >(2475-2035 )/601)

=P(Z>0.73) =0.2327 (from standard normal table)

Answer: 23.27%

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(b)What percent spend between $2,475 and $3,150 per year on reading and entertainment?

P(2475<X<3150) = P((2475-2035 )/601 <Z< (3150-2035 )/601)

=P(0.73<Z<1.86)

=0.2013 (from standard normal table)

Answer:

20.13%

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(c)What percent spend less than $1,025 per year on reading and entertainment?

P(X<1025) = P(Z<(1025-2035 )/601)

=P(Z<-1.68) =0.0465 (from standard normal table)

Answer:

4.65%

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