Question

Suppose that a Trader Joe's customer selected at random, spends on the average $60 with a standard deviation of $10. Assume also that the corresponding probability distribution is normal.

a) Find the (perhaps, approximate) probability that a customer selected at random spends less than $70.
options:
0.95
0.5
0.75
0.84
b) Find the (perhaps, approximate) probability that a customer selected at random spends more than $70.
options:
0.11
0.76
0.16
0.1
c) Find the (perhaps, approximate) probability that a customer selected at random spends less than $50.
0.16
0.11
0.23
0.05
d) Find the (perhaps, approximate) probability that the amount a customer selected at random spends falls between $50 and $70.
options:
0.32
0.5
0.1
0.68
e) 5% of customers spend less than what amount? (The answer may present an approximate value.)
options
$30.5
$20.6
$20
$43.5

Answer 1

0.84

0.16

0.16

0.68

$43.5

Explanation:

μ = 60

σ = 10

(a)

`Z=(x-\mu)/(\sigma)`

`=(70-60)/(10)`

`=1`

P(Z < 1) = 0.84

(b)

P(Z > 1) = 1 - P(Z < 1)

= 1 - 0.84

= 0.16

(c)

`Z=(x-\mu)/(\sigma)`

`=(50-60)/(10)`

`=-1`

P(Z < -1) = 0.16

(d)

P(-1 < Z < 1) = P(Z < 1) - P(Z < -1)

= 0.84 - 0.16

= 0.68

(e)

P(Z < z) = 0.05

z = -1.645

`Z=(x-\mu)/(\sigma)`

`-1.645=(x-60)/(10)`

`-1.645*10=x-60`

`x=-16.45+60`

`= 43.55`