Question

The retail price of a particular model of a smartwatch has a skewed distribution with mean $220 and standard deviation $15. Suppose that you check the retail prices of this smartwatch at randomly selected 33 stores and calculate the sample mean price.(1) What distribution will the sample mean have in this setting?

(a) Exact normal distribution

(b) Approximate t distribution

(c) Approximate normal distribution

(d) Standard normal distribution

(e) Exact t distribution

(2) What is the probability that the sample mean of 33 smartwatches is between $217 and $222?

Answer 1

1)

(c) Approximate normal distribution (since sample size >=30 and population is not normal)

2)

for normal distribution z score =(X-μ)/σ
here mean=       μ=	220
std deviation   =σ=	15.000
sample size       =n=	33
std error=σx̅=σ/√n=	2.61116

probability =P(217<X<222)=P((217-220)/2.611)<Z<(222-220)/2.611)=P(-1.15<Z<0.77)=0.7794-0.1251=0.6543