Answer
0
Work Step by Step
Μ=87, σ=22
a. $P(x \gt 114 )$ = $P(z \gt \frac{114-87}{22} )$ = $P(z \gt 1.2273 )$ = 0.1099
b. $P(40 \leq x \leq 60 )$ = $P(\frac{40-87}{22} \leq z \leq \frac{60-87}{22})$ =$P(-2.1364\leq x \leq -1.2273 )$ =0.1099-0.0163= 0.0936=
=9.36%
c. $P(70 \leq x \leq 105 )$ = $P(\frac{70-87}{22} \leq z \leq \frac{105-87}{22})$ =$P(-0.7727\leq x \leq 0.8182 )$ =0.7934-0.2198= 0.5736
=57.36%
d. $P(x \geq 185)$
$P(x \geq 185)$ : z = $\frac{185-87}{22}$ =4.4545
$P(z \geq 4.4545)$ = 0
It is impossible for a customer paying by check to spend more than 15 dollars because the probability shown is 0.
