# For standard normal random variable Z, determine the value of constant c which makes the probability statements given below correct

For standard normal random variable Z, determine the value of constant c which makes the probability statements given below correct
a) $\mathrm{\Phi }\left(c\right)=0.8888$
b) $P\left(0\le Z\le c\right)=0.334$
c) $P\left(-c\le Z\le c\right)=0.488$
e) $P\left(c\le |Z|\right)=0.154$
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Zackary Galloway
Step 1
a) $\mathrm{\Phi }\left(c\right)=0.8888\phantom{\rule{0ex}{0ex}}⇒P\left(Z\le c\right)=0.8888$
From standard norma tables, the value corresponding to 0.8888 cumulative probability is 1.22
Hence, $c=1.22$
Step 2
b)
From standard normal tables, the value corresponding to 0.8888 cumulative probability is 0.97
Hence, $c=0.97$
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Kody Whitaker
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c) $P\left(c\le Z\right)=0.271\phantom{\rule{0ex}{0ex}}⇒P\left(Z\ge c\right)=0.271\phantom{\rule{0ex}{0ex}}⇒1-P\left(Z
From standard norma tables, the value corresponding to 0.729 cumulative probability is 0.61
Hence, $c=0.61$
d)
Hence, $c=0.66$
e)
From standard normal tables, the value corresponding to 0.577 cumulative probability is 0.194
Hence, $c=0.19$